2D Geometry Questions and Answers

Point R divides EF in the ratio 1:5. If the coordinates of Eand Fare (4, 8) and (11,4), respectively, what are the coordinates of Rto two decimal places? A. (4.66, 7.62) B. (6,6.86) C. (5.17,7.33) D. (9.83, 4.67)

Find x so that the triangle with vertices A=(-4, 3, -2), B=(-6. -1, -9), and C-(-9, 7, x) has a right angle at A. x=_________

5. If (ACBD)=-1, and M is the midpoint of AB show that 1/CA CB+ 1/DA DB=1/MA MB

Determine whether each statement is true or false. a. The Poincaré Incidence Plane is an example of an affine plane.

If P and Q are points and the Ruler Postulate is assumed to be true, prove the following. a. PQ ≥ 0 b. PQ = 0 if and only if P = Q C. PQ = QP

Follow these steps to construct a diagram: 1. Draw a circle with center A that takes up most of the visible view. 2. Create four well-spaced points on circle A. Label them B, C, D, and E, in clockwise alphabetical order. 3. Create two chords, BD and CE, and mark F as their point of intersection. 4. Measure and record BF, CF, DF, and EF. Also record m<CFB. 5. Draw four line segments, AB. AC. AD, and AE. (To highlight them for later use, try making these line segments different colors by changing the object properties.) 6. Label the central angles CAB and LEAD, and display their measures.

Find the parametric equation of a plane perpendicular to a given straight line passing through point P. I want to know how to solve both problems (1) and (2). (1) P(-2, 1, 7), *=x-4 /2 = y-2 /-3 = z /-5 (2) P(1, 1, -2), x-2/-3= y-3/-2 = -z-1

Enter the standard graphing form of the horizontal parabola for the given vertex and directrix. Vertex: (4,-4) Directrix: x = 4 - 1/-12

For an arc length s, area of sector A, and central angle 0 of a circle of radius r, find the indicated quantity for the given value. r=2.32 in, θ=pi/2 s=?

Given: a circle with a center O and a straight line with a point M on it (they do not intersect). Construct a circle tangent to the given circle and tangent at point M to the given line.

Smog is a general term used to describe pollutants in the air. A smog alert is usually issued when the air quality index is greater than 50. Air quality can vary throughout the day, increasing when more cars are on the road. Consider a model of the form 1= 30 sin (15(t - 4)) + 25 Where I is the value of the air quality index and t measures the time after midnight, in hours. a.What is the period of the modelled function? Explain why this makes sense. b.Determine the maximum, minimum and amplitude. c.What is the value of the air quality index at 6am?

What is the most specific name of the quadrilateral formed by the coordinates (-2,0), (-1,5), (0,4)(-3,1)? select one: O Rectangle O Parallelogram O Square O Rhombus

A line segment has an endpoints at (-5, 1), and (5,6). What is the location of the point that divides the segment in a ratio of 4:6? Select one: O (4,5.5) O (3,5) O (-3,2) O (-1,3)

A line segment has an endpoints at (4.25, 19) and (8, -1). What is the location of the point that divides the segment in a ratio of 1:4? O (3,7.25) O (5.75, 11) O (5,15) O (-6.5,7)

A line segment has an end points at (-5, 1) and (5,6). What is the location of the point that divides the segment in a ratio of 2:8? Select one: O (-1,3) O (3,5) O (-3,2) O (4,5.5)

Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: x (t)= - 5t² y(t)= -7 + 5t The resulting equation can be written as x =

Find the area of the sector of a circle with radius 4 inches formed by a central angle of 5°: ________square inches Round your answer to two decimal places.

A 30-ft ladder leans against a building so that the angle between the ground and the ladder is 80°. How high does the ladder reach on the building?

2) Given that angle 1 and angle2 are supplementary, angle 2 and angle 3 are supplementary, prove that angle1 is congruent to angle 2.

Which of the following is the best definition of vertical angles? Answer O Two angles having measures that sum to 180° O Opposite, congruent angles formed when two lines intersect O Two angles having measures that sum to 90° O Two angles that share a common side O None of the above

. Graph by hand (upload photo) the function and identify the following: o x-intercept o vertical asymptote o horizontal asymptote o hole o domain o range f(x)=(x+2)/(x²-3x-10)

Find the points where three circles intersect. Choose the center points and radii randomly by yourself. Solve on paper or do it on Matlab.