# Coordinate system Questions and Answers

Math

Coordinate systemDetermine what type of transformation is represented.
A. reflection
B. translation
C. rotation
D. none of these

Math

Coordinate systemExplain in words how each of the following functions are related to y = √x and then sketch all five graphs on the same set of axes including the parent function. Be sure to identify which graph is which either by labeling or using different colours
(a) y = √x-3 + 4
(b) y = -√x-2 + 1
(c) y = √-x+4 - 3
(d) y = 2√x - 5

Math

Coordinate systemDirections - Write an equation in Slope-Intercept Form (y = mx + b) for the line with the given slope (m) and y-intercept (b).
m = 4,b=-3

Math

Coordinate systemSolve the following system by graphing.
x+y-6=0
x-y=0
What is the solution of the system?
(3,3)
(-3,3)
(3,-3)

Math

Coordinate systemSolve the following system of equations.
3x+2y-5=0
x=y+10
Make sure there are NO SPACES in your answer. Include a comma in your answer.

Math

Coordinate systemFor the following system, use the second equation to make a sub
x + 5y - 10 = 0
x= 2y-8
What is the resulting equation in simplest form?
-3y-18-0
3y-18-0
7-18-0

Math

Coordinate systemA grid shows the positions of a subway stop and your house. The subway stop is located at (7, -7) and your house is located at (-3, 3). What is the distance, to
the nearest unit, between your house and the subway stop?
11
14
19
24

Math

Coordinate systemAn architect is designing a garden for a client on a planning sheet. The client requests the relocation of a water fountain by the rule (x,y) → (x+ 9, y-8). Later, the client decides that they would prefer the water fountain's location moved from this new position 5 units left and 3 units down. Find the composition as a single transformation.
A. (x,y) → (x+4, y-11)
B. (x,y) → (x+6, y-13)
C. (x, y) → (x + 14, y − 5)
D. (x, y) → (x-3, y-5)

Math

Coordinate systemWhich set of ordered pairs has point symmetry with respect to the origin (0, 0)?
(-12, 5), (12,5)
(-12, 5), (-12,-5)
(-12, 5).(-5, 12)
(-12, 5), (12,-5)

Math

Coordinate systemFind the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below.
Find the regression equation.

Math

Coordinate systemOne line passes through the points (-8,1) and (4,4). Another line passes through points (-9, -7) and (9.-3).
Are the lines parallel, perpendicular, or neither?
Choose 1 answer:
Parallel
Perpendicular
Neither

Math

Coordinate systemThe vertices of ΔJKL have coordinates J(5, 1), K(-2, -3), and L(-4,1). Under which transformation is the image ΔJ'K'L' not congruent to ΔJKL?
(A) a translation of two units to the right and two units down
(B) a counterclockwise rotation of 180 degrees around the origin
(C) a reflection over the x-axis
(D) a dilation with a scale factor of 2 and centered at the origin

Math

Coordinate systemWhat's the slope and y-intercept of the graph of 7x+y=8?
A) Slope-7, y-intercept = 8
B) Slope 7, y-intercept = 8
C) Slope = -8, y-intercept = 7
D) Slope = -7, y-intercept = -8

Math

Coordinate systemIf a translation maps point (3, 2) to (4, 5); or T: (3, 2) (4, 5), indicate the image for (2, 4).
(3.7)
(2, -1)
(5, 3)

Math

Coordinate systemThe longer base of an isosceles trapezoid joins points (-3, -2) and (7, -2). One endpoint of the shorter base is (-1, 4). What are the coordinates of the other endpoint?
(0, -3)
(5,4)
(4, 5)

Math

Coordinate systemA boat heads directly north across a river, 68 m wide at a rate of 3 m/s. The current is flowing downstream (due west) at 1.9 m/s.
A. What is the resultant velocity and direction of the boat? Write your angle as a bearing.
B. How long does it take the boat to cross the river? (Hint: How long does it take to covert the vertical distance of 68m across the river?)
C. How far downstream is the boar when it reaches the other side of the river?

Math

Coordinate systemAn equation for the line L is:
y = 11 + 10/7 (x-4)
The angle I makes with the x-axis is:

Math

Coordinate systemIf P (3,2), find the image of P under the following rotation. 180° counterclockwise about the origin

Math

Coordinate systemThe y-intercept of the parent quartic function, f(3) = 4, is translated 3 units to the right and 1 unit down. Which equation represents this transformation?
A g(t) = (x-3)^4 - 1
B. g(t) = (x+3)^4 - 1
C. g(s) = (x-1)^4 +3
D. g(x) = (x+1)^4 +3

Math

Coordinate systemWhat is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0?
4x-y-6=0
4x+y+6=0
4x+y-6=0

Math

Coordinate systemThe vertices of a rectangle are R(-5, -5), S(-1,-5), T(-1, 1) and U(-5, 1). After R' is the point (3, 0). Find the translation and coordinates of U'. translation,
[A] (8,-5); (3,-4)
[B] (5,-8); (0,-7)
[C] (-5, 8); (-10, 9)
[D] (8,5); (3, 6)

Math

Coordinate systemThe revolving restaurant on top of a hotel in San Francisco, California takes 45 minutes to complete a full counterclockwise rotation. A table that is 30 ft from the center of the restaurant starts at position (30, 0). What are the coordinates of the table after 9 minutes? Round to the nearest tenth.
(9.3, 28.5)
(11.3, 17.3)
(28.5.9.3)
(23, 19.3)

Math

Coordinate systemEstimate the solution to the following system of equations by graphing.
3x + 5y = 14
6x - 4y = 9

Math

Coordinate systemThe point (7,-4) is on the terminal arm of angle θ in standard position.
a) Draw a sketch of angle θ. Be sure to label the side lengths and θ.
b)Determine the exact values of sin θ, cos θ, and tan θ.
c) State the value of θ, to the nearest degree.

Math

Coordinate systemThe polar coordinates of a point are (9,3π/2). Find the rectangular coordinates of this point.
The rectangular coordinates are
(Simplify your answer. Type an ordered pair. Type an exact answer for each coordinate, using radicals as needed. Use integers or fractions for any numbers in the expression.)

Math

Coordinate systemThe vertex form of the equation of a horizontal parabola is given by z= 1/4p(y-k)2+h, where (h, k) is the vertex of the parabola and the
absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use GeoGebr
to create a horizontal parabola and write the vertex form of its equation. Open GeoGebra , and complete each step below.
Part A
Mark the focus of the parabola you are going to create at R(-5, 2). Draw a vertical line that is 8 units to the right of the focus. This line will be the
directrix of your parabola. What is the equation of the line?

Math

Coordinate systemSuppose a point has polar coordinates (6, 2π/3) with the angle measured in radians.
Find two additional polar representations of the point.
Write each coordinate in simplest form with the angle in [-2π, 2π].

Math

Coordinate systemRectangle HIJK is dilated to produce rectangle H'T'J'K'. If the perimeter of HIJK is a and the perimeter of H'I'J'K' is b, what is the scale factor of the dilation?

Math

Coordinate systemFairview is hosting a city-wide arts festival at which vendors can pay to have a small booth or a large booth. The fee for a small booth is $27, whereas the fee for a large booth is $81. The city hopes to receive at least $1,500 in fees.
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of small booths
y = the number of large booths
(27+ x)(81+ y) ≥ 1,500
27x 81y 2 1,500
27 + x +81 + y ≥ 1,500
27x+81y 2 1,500

Math

Coordinate systemIf you flip the reciprocal parent function, F(x) = 1/x, across the y-axis, what is
the equation of the new function?
A. G(x) = -¹/-x
B. G(x) = 1/x-1
C. G(x) = 1/x - 1
D. G(x) = x

Math

Coordinate systemIf you apply the transformations below to the quadratic parent function, F(x) = x², what is the equation of the new function?
Shift six units right.
Shift four units down.
A. G(x) = (x-6)²-4
B. G(x) = (x-4)² +6
C. G(x) = (x-4)²-6
D. G(x) = (x+6)² - 4

Math

Coordinate systemChoose the best definition of SAS Similarity.
When two triangles have corresponding angles that are congruent and the included corresponding sides with identical ratios.
None of the other answers are correct
Sides that are in the same position in different plane figures.
When two triangles have corresponding angles that are congruent, the triangles are similar.
the result of a transformation.

Math

Coordinate systemA directed line segment begins at F(-10, -4), ends at H(8, 4), and is divided in the ratio 6 to 2 by G.
What are the coordinates of G?
(3.3, 5)
None of the other answers are correct
(-1.6, 5)
(3.5, 2)
(2.5, 2)

Math

Coordinate systemA scientist concerned about dehydration of soccer players on hot days measured the fluld consumption of twenty-six
soccer players. The mean fluid consumption per day was 2,780 milliliters with a standard deviation of 567 milliters.
What is the probability that a player consumed between 1,646 and 3,347 milliliters? Use the 68-95-99.7 normal
distribution curve.
97.35%
81.5%
83.85%
81.3%

Math

Coordinate systemSolve the following system of equations.
2x² + 4y² = 132
5x² – 5y² = −45
Solution(s):

Math

Coordinate systemWhat is the area of a rectangle with vertices located at (-1, 1), (-1,-4), (5, -4), and (5, 1)?
20 square units
12 square units
15 square units
30 square units

Math

Coordinate systemGraph, label, and connect the following points: S(3, 2), D(6, 8), I(2, 8), and E(15, 2) to form polygon SIDE.
a. Name the type of polygon.
b. Find the length of the height.
c. Find the area of the figure named SIDE.
d. Calculate the lengths of segments SI and DE.
e. Calculate the perimeter of SIDE. f. Find the slopes of SI and DE.

Math

Coordinate systemWhich of the following most accurately describes the translation of the graph: y=(x-7)² + 16, from
the origin (0, 0)?
Select one:
7 units down, 16 units right
7 units up, 16 units right
16 units up, 7 units left
16 units up, 7 units right

Math

Coordinate systemPoints (4, 5) and (10, 5) are vertices of a rectangle.
The length of the rectangle is twice the width.
The other vertices are located at (4,) and (10,). What could these ordered pairs be?

Math

Coordinate systemWhat is the image point of (9, 0) after a translation left 2 units and up 5 units?

Math

Coordinate systemThe point H is plotted on the coordinate grid below. Plot the point H', the reflection of H over the x-axis. on the graph to plot a point.

Math

Coordinate systemYour candy factory makes Sticker Bars and N&N's. For each case of Stickers, you make $40 profit. For each case of N&N's, you make $55 profit. It takes 2 machine-hours to make Stickers and 5 man-hours to produce one case of candy. It takes 6 machine-hours to make N&N's and 4 man-hours to produce one case of candy. The total number of hours cannot exceed 150 machine-hours and 155 man-hours. Find the number of each type of candy that can be produced in order to maximize profit. Then determine the profit.

Math

Coordinate systemThe number of hamburgers, and number of sodas, y, that Shaquile can purchase with $12 is represented by the inequality
4x + 2y ≤ 12
Which coordinate pair(s) (x, y) represent a possible number of hamburgers and sodas that Shaquile can purchase? Select all that apply.

Math

Coordinate systemf(x)=2x³+2x²-8x-8
If there is more than one answer, separate them with commas.
Click on "None" if applicable.

Math

Coordinate systemThe parent cosine function is shifted 5 units left, then vertically stretched by a factor of 4 and shifted up 2 units. Which statement is true about the graph of the transformed function?
A. The midline is y = 2.
B. The midline is y = 4.
C. The midline is y = 8.
D. The midline is y = 5.

Math

Coordinate systemGraph the solution to the following system of inequalities.
2x+5y>-20
-2x+7y<-21
Then give the coordinates of one point in the solution set.

Math

Coordinate systemWhich of the following equations display=
Select all that apply:
r = 2sin θ+5θ
T = -sinθ
T = 5sin²θ+3cos²θ + 5sinθ+θ
r = -sin²θ + 4θ+5
T = = -4cos²θ-sinθ + 2θ
symmetry based on the test for θ =
symmetry? Select all that apply.

Math

Coordinate systemΔABC is reflected across the x-axis and then translated 4 units up to create ΔA'B'C. What are the coordinates of the vertices of ΔA'B'C?
A. A'(-3, 3), B'(-1, 1), C'(-2, 3)
B. A'(3, -3), B'(1, -1), C'(2, -3)
C. A'(3, -5), B'(1, -7), C'(3, -5)
D. A'(-3, 3), B'(-1, 1), C'(-2, -3)

Math

Coordinate systemSelect the different types of transformations you can have with a function:
Select one or more:
a. Reflection about y axis
b. Reflection about origin
c. Reflection about x axis
d. Horizontal Shifts
e. Bolding
f. Restriction
g. Reflection about line y=x
h. Shading
i. Stretching
j, Vertical Shifts
k. Compression