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

Question

and a center point of dilation at the origin

Answer 1

To 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, we need to multiply the x and y coordinates of each point by 3.

Coordinates of A:
x-coordinate of A' = -2 * 3 = -6
y-coordinate of A' = -2 * 3 = -6

Therefore, A' is located at (-6, -6).

Coordinates of B:
x-coordinate of B' = -4 * 3 = -12
y-coordinate of B' = -3 * 3 = -9

Therefore, B' is located at (-12, -9).

Coordinates of C:
x-coordinate of C' = -2 * 3 = -6
y-coordinate of C' = -5 * 3 = -15

Therefore, C' is located at (-6, -15).

The coordinates of A', B', and C' after the dilation 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.

Answer 3

To find the scale factor needed to dilate a square with a side length of 8 units to create a square with a side length of 20 units, we need to divide the side length of the larger square by the side length of the smaller square.

Scale factor = side length of larger square / side length of smaller square
Scale factor = 20 units / 8 units
Scale factor = 2.5

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

Answer 4

You use scale factor of 3/4 to create a dilated circle with a radius of 9 inches. What is the radius of the original circle?

Answer 5

To find the radius of the original circle, we need to divide the radius of the dilated circle by the scale factor.

Scale factor = 3/4
Radius of dilated circle = 9 inches

Radius of original circle = Radius of dilated circle / Scale factor
Radius of original circle = 9 inches / (3/4)
Radius of original circle = 9 inches * (4/3)
Radius of original circle = 12 inches

Therefore, the radius of the original circle is 12 inches.

Answer 6

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

Answer 7

Since triangle CDE is similar to triangle PQR, the corresponding angles are equal. Therefore, the measure of angle P would be 13° and the measure of angle Q would be 65°.

To find the measure of angle R, we can use the fact that the sum of the angle measures in a triangle is 180°.

m∠P + m∠Q + m∠R = 180°

Substituting the known values:

13° + 65° + m∠R = 180°

78° + m∠R = 180°

Subtracting 78° from both sides:

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°