2D Geometry Questions and Answers

What is the radius of the circle x² + y² - 100 = 0? Simplify any fractions.

What is the center of the circle x² + y² - 36= 0? Simplify any fractions

Find the x-intercepts of the parabola with vertex (1,-9) and y-intercept at (0,-6). A. (-1,0), (3,0) B. (-0.73,0), (2.73,0) C. (-1.48,0), (2.48,0) D. (-4.67,0), (1.67,0)

In ΔABC, if sin A =4/5 and tan A=4/3, then what is cos A? A. 3/5 B.4/5 C.3/4 D.5/3

What is the radius of the circle x² + y² - y - 30 = 0? Write your answer in simplified, rationalized form.

What is the center of the circle x² + y² - 5x - 14 = 0? Simplify any fractions.

Radius OA of circle O has a slope of 2.5. What is the slope of the line tangent to circle O at point A? A. 0.8 B. 2.5 C. -0.4 D. -5

What is the center of the circle x² + y² - 81 = 0? Simplify any fractions.

Type the correct answer in each box. The general form of the equation of a circle is x2 + y2 +8x+22y+37= 0. The equation of this circle in standard form is (x+ )² + (y+ )² = The center of the circle is at the point

35 Quadrilateral PQRS has vertices P(-2,3), Q(3,8), R(4,1), and S(-1,-4). Prove that PQRS is a rhombus. [The use of the set of axes on the next page is optional.] Question 35 continued. Prove that PQRS is not a square. [The use of the set of axes below is optional.]

Quadrilateral ABCD has diagonals AC and BD. Which information is not sufficient to prove ABCD is a parallelogram? (1) AC and BD bisect each other. (2) AB CD and BC = AD (3) AB = CD and AB || CD (4) AB = CD and BC|| AD

Suppose a circle is divided into congruent slices. Match each number of slices with the resulting central angle measure of each slice. 2 3 4 5 6 8

In a right trapezoid ABCD, <A = <D = 90deg, AB <CD, we know: AB = 9cm, CD = 12cm and AD = 4cm. Find the distance from B to AC and the tangent of the acute angle of the trapezoid.

∠DEH is adjacent to ∠HEG. ∠DEG is 106° and ∠HEG is 55°. Find the measure of ∠DEH.

∠JKL is adjacent to ∠LKM. ∠JKL is 15° and ∠LKM is 35º. Find the measure of ∠JKM.

∠PQR is adjacent to ∠RQS. ∠PQS is 110° and ∠RQS is 34°. Find the measure of ∠PQR.

Find the limit of the geometric series 200+50 +12.5+...

Consider a segment AB and two points O and O' on the same side of AB. Prove that the image of AB after two successive half-turns, first about O and then about O' is parallel to AB. Assume Euclidean.

26. Two polygons are similar. The perimeter of the smaller polygon is 66 m and ratio of their corresponding side lengths is 3/4. Find the perimeter of the larger polygon. (A) 33 m (B) 49.5 m (C) 132 m (D) 88 m

Solve for x. 2x³ = 18x x = [?], [ ], [ ]

Determine if each statement must be true, could possibly be true, or definitely can't be true. Explain or show your reasoning. 1. Congruent figures are similar. 2. Similar figures are congruent.

A six-sided polygon is called A. a nonagon B. a quadrilateral C. a heptagon D. a hexagon

Graph the compound inequality: y≤ 3/4 x+ 2 x≥-4

In circle F with m∠EFG = 70 and EF = 19 units, find the length of arc EG. Round to the nearest hundredth.

Which is the best description of congruent line segments? perpendicular line segments line segments that are parallel line segments that have the same length line segments that share a vertex u will need this Theorem to answer the next question. The triangle angle bisector theorem states that in a triangle, the angle Disector of any angle will divide the opposite side in the ratio of the sides containing the angle. Consider the figure below:

A square has a side length of 10 inches. What is the length of the diagonal of the square? You may draw a picture to help. Round your final answer to the nearest tenth. diagonal length =___ inches

Parabola A and parabola B both have the x-axis as the directrix. Parabola A has its focus at (3, 2) and parabola B has its focus at (5, 4). Select all true statements. A. Parabola A is wider than parabola B. B. Parabola B is wider than parabola A. C. The parabolas have the same line of symmetry. D. The line of symmetry of parabola A is to the right of that of parabola B. E. The line of symmetry of parabola B is to the right of that of parabola A.

Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.] A. 39.84 units² B. 46.11 units² C. 44.28 units² D. 36.38 units2

Find the missing the side of the triangle. A. 4√2 m B. √130 m C. √179 m D. √211 m

Quadrilatera ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 24 feet, 16 feet, and 12 feet long. If the two shortest sides of quadrilateral EFGH are 9 feet long and 18 feet long, how long is the 2nd longest side on quadrilateral EFGH? A. 24 feet B. 16 feet C. 20 feet D. 36 feet

Find the distance between the points (0, 10) and (-9, 1). A. 12.73 B. 14.21 C. 16.23 D. 20.22

What type of triangle has side lengths 4, 4√15, and 16? A. acute B. not a triangle C. obtuse D. right

If the length of one leg of a right triangle is 3 and the hypotenuse is √34, what is the length of the other leg? A. 8 B. 5 C. 34 D. √43

Which of the following is the rule for rotating the point with coordinates (x,y). 180° clockwise about the origin? A. (x,y) → (y,x) B. (x,y) → (-y, -x) C. (x,y) → (-x, y) D. (x,y) → (y, -x)

If BD≅ BC, BD = 5x-26, BC= 2x + 1, and AC = 43, find AB.

Given: Parallelogram ABCD with diagonal A Prove: ∠D congruent to ∠B You may not use the theorem stating that opposite angles of a parallelogram are congruent.

Similar Triangles Theorem 128. For triangles T and T', the following are equivalent; that is, each one implies the other two. (i) T is similar to T', that is, T is congruent to a dilation of T' (ii) Each angle of T is congruent to the corresponding angle of T' (iii) The sides of T are proportional to the sides of T'.

Theorem 111. Dilations preserve angle measure. Specifically, if noncollinear points A, B and C go to (necessarily) non-collinear points A', B' and C' under a dilation, then ∠ABC = ∠A'B'C'. [Draw a diagram and apply what you know.] The definition of a dilation says that the length of each segment coming from the center O is multiplied by the scaling factor k, that is, L(OP')=kL(OP). We would like to find out if the same relationship holds for every segment.

Given the points C(-1,-5) and D(-7, 11), find the coordinates of point E on CD such that the ratio of CE to ED is 5:3.

Find the equation of the hyperbola with vertices V(0, 2) and V'(4, 2) with one minor point at M(2, 3).

Two LORAN radio stations A and B are 190 kilometers apart and send a simultaneous radio signal to a ship. The signal from B arrives 0.0002 seconds before the signal from A. If the signal travels 300,000 kilometers per second, find the equation of the hyperbola on which the ship is positioned. Use a coordinate system where the origin is the midpoint between the stations, and the stations lie on the x-axis.

Two tangent lines at the endpoints of a given arc containing 120° are drawn, and a circle is inscribed into the figure bounded by these tangent lines and the arc. Prove that the circumference of this circle is equal to the arc length of the given arc.

Critical thinking. In ⊙ R, the measure of arc AB = 60°, the measure of arc BC 25°, the measure of arc CD = 70°, and the measure of arc DE 20°. Find two possible values for the measure of arc AE.

Use the information provided to answer Part A and Part B. Justify your answer using the CER method for part A as follows: Claim - The y - coordinate of the center of the circle is____ Evidence - Show work used to solve for/find the y coordinate. Reasoning - Use the work you showed in "Evidence" to justify your "Claim". Come up with your own CER response for part B. The equation x^2 + y^2 - 4x + 2y = b describes a circle. A)Determine the y-coordinate of the center of the circle. b)The radius of the circle is 7 units. What is the value of b in the equation?

The rectangle on the right is a scaled copy of the rectangle on the left, Identify the scale factor. Express your answer as a whole number or fraction in simplest form, first rectangle second rectangle l=14,b=6 l=56,b=24

The jar on Mrs. Wilson's desk contains 20 green paper clips, 30 red paper clips, 15 white paper clips, and 10 black paper clips. She selects a paper clip without looking, does not replace it, and selects another. Determine each probability. Show complete work on your worksheet!!! (a) P(both paper clips are white) = Fractional set up:________________ 2 decimal places:________________ (b). P(second paper clip is green if first paper clip is black) = Fractional set up:_______________ 2 decimal places:_______________ (c). P(second paper clip is green if first paper clip is green) = Fractional set up:_______________ 2 decimal places:_______________

32 Triangle ABC has vertices with coordinates A(-1,-1), B(4,0), and C(0,4). Prove that ABC is an isosceles triangle but not an equilateral triangle. [The use of the set of axes below is optional.]

Using words + diagrams as needed, describe how you would construct the length (3+√7)/2 using only compass and straightedge. It will be helpful to split this construction into a few steps.

How many triangles are there that have a = 7, b=5, and area 5√5. There is/are _____ triangle(s). (Type a whole number.)

The points (3, 1) and (6,5) are the endpoints of a radius of a circle, and the point (9, 2) is inside the circle. Write the standard equation of the circle. (x - _____)^2 + (y - _____)^2 = (______)^2