Triangle ABC has vertices point A(−2,−2) , point B(−4,−3) , and point C(−2,−5) . Find the coordinates of A′ , B′ , and C′ after a dilation with a scale factor of 3 and a center point of dilation at the origin.(2 points)

Question

A′= (
)
B′= (
)
C′= (
)

Answer 1

To find the coordinates of the vertices A', B', and C' after a dilation with a scale factor of 3 and a center point at the origin, we need to multiply the coordinates of the original vertices by the scale factor.

For point A(−2,−2):
A' = (−2*3, −2*3) = (−6, −6)

For point B(−4,−3):
B' = (−4*3, −3*3) = (−12, −9)

For point C(−2,−5):
C' = (−2*3, −5*3) = (−6, −15)

Therefore, the coordinates of A', B', and C' are:
A′ = (−6, −6)
B′ = (−12, −9)
C′ = (−6, −15)

Answer 2

If you would like to dilate a square with a side length of 8 units to create a square with a side length of 20 units, what scale factor should you use? Write your answer in decimal form.(1 point)

Answer 3

To find the scale factor needed to dilate the square with a side length of 8 units to create a square with a side length of 20 units, we can use the formula:

Scale factor = New side length / Original side length

In this case, the new side length is 20 units and the original side length is 8 units:

Scale factor = 20 / 8
Scale factor = 2.5

Therefore, the scale factor needed to dilate the square is 2.5.

Answer 4

You use scale factor of 34 to create a dilated circle with a radius of 9 inches. What is the radius of the original circle?(1 point)

Answer 5

To find the radius of the original circle given that a scale factor of 34 was used to create a dilated circle with a radius of 9 inches, we can use the formula:

New radius = Scale factor * Original radius

In this case, the scale factor is 34 and the new radius is known to be 9 inches. Let's denote the original radius as r:

9 = 34 * r

Now, we can solve for the original radius r:

r = 9 / 34
r ≈ 0.2647

Therefore, the radius of the original circle is approximately 0.2647 inches.

Answer 6

△CDE∼△PQR . m∠C=13° , m∠D=65° . What are the measures of angles P , Q , and R ?(2 points)
m∠P =
°, m∠Q =
° and m∠R=
°

Answer 7

Since triangles CDE and PQR are similar, corresponding angles are congruent.

Given:
m∠C = 13°
m∠D = 65°

Therefore:
m∠P = m∠C = 13°
m∠Q = m∠D = 65°

Since the sum of the interior angles of a triangle is always 180°, we can find the measure of angle R:

m∠R = 180 - (m∠P + m∠Q)
m∠R = 180 - (13 + 65)
m∠R = 180 - 78
m∠R = 102°

Therefore, the measures of angles P, Q, and R are:
m∠P = 13°
m∠Q = 65°
m∠R = 102°

Answer 8

△XYZ∼△RST . m∠X=50° , m∠S=79° . What is the measure of angle T ?(1 point)
m∠T =
°

Answer 9

Since triangles XYZ and RST are similar, corresponding angles are congruent.

Given:
m∠X = 50°
m∠S = 79°

Therefore:
m∠T = m∠X = 50°

Therefore, the measure of angle T is 50°.