Triangle hjk is transformed to similar triangle h’j’k’: a coordinate plane is shown. triangle hjk has vertices h at 8 comma 8, j at 8 comma 4, and k at 4 comma 4. triangle h prime j prime k prime has vertices h prime at 2 comma 2, j prime at 2 comma 1, and k prime at 1 comma 1. what is the scale factor of dilation? 1 over 2 1 over 3 1 over 4 1 over 5

We are given coordiates of vertices of triangle ΔHJK as H(8,8), J(8,4), K(4,4)

and coordinates of transformed triangle ΔH’J’K are H'(2,2), J'(2,1), k'(1,1).

We can clealry see that if we divide each value in coordinate by 4, we get the coordinates of the transformed triangle.

Let's see, what's dilation being applied there : H(8,8) ---> 1/4 (8,8) = H' (2,2) ,

J(8,4) ---> 1/4(8,4) = J'(2,1) and

K(4,1) ---> 1/4 (4,4) = K'(1,1).

So, we can clearly see that each coordinate is being multiplied by 1/4.

So, we can say the scale factor of dilation is 1 over 4, that is 1/4.

a. is correct

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°