Question

60 PTS!! WILL GIVE BRAINLIEST!! PLZ HELP!!!

AB has endpoints at (-9, 12) and (3, -6). Its transformation A'B' has endpoints at (-3, 4) and (1, -2). What type of transformation occurred? Are lengths of segments affected by this type of transformation? Explain.
A) reflection; no; The lengths of the two segments are the same.
B) rotation; yes; The length of segment A'B' is longer than the original segment AB.
C) dilation by a scale factor of 3; yes; The length of segment A'B' is shorter than the original segment AB.
D) dilation by a scale factor of 1/3; yes; The length of segment A'B' is shorter than the original segment AB.
**I'm giving 60 point but I will report unnecessary answers

Answer 1

Answer:

D

Step-by-step explanation:

Let's see if the lengths of these two segments are the same or not. We will use the distance formula, which says that for two points $(x_1,y_1)$ and $(x_2,y_2)$, the distance between them is: $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$.

For AB, $(x_1,y_1)$ is (-9, 12) and $(x_2,y_2)$ is (3, -6). So, the distance is:

$\sqrt{(-9-3)^2+(12-(-6))^2}=\sqrt{(-12)^2+(18)^2} =\sqrt{144+324} =\sqrt{468}$ $=6\sqrt{13}$

For A'B', $(x_1,y_1)$ is (-3, 4) and $(x_2,y_2)$ is (1, -2). So, the distance is:

$\sqrt{(-3-1)^2+(4-(-2))^2}=\sqrt{(-4)^2+(6)^2} =\sqrt{16+36} =\sqrt{52}=2\sqrt{13}$

We can see that $6\sqrt{13}$ is 3 times of $2\sqrt{13}$, which means that AB (the original) is 3 times the length of A'B' (the transformed).

Since the length has changed, we know that it must be some sort of dilation because that's the only kind of transformation that will change the length. We see that the segment has also shortened, which means that its scale factor must be less than 1.

The only answer that matches is D.

Hope this helps!

Answer 2

Answer:

D) dilation by a scale factor of 1/3; yes; The length of segment A'B' is shorter than the original segment AB.

Step-by-step explanation:

From:

(-9, 12) and (3, -6)

To:

(-3, 4) and (1, -2).

(-3,4) = ⅓(-9,12)

(1,-2) = ⅓(3,-6)

It's a dilation with factor ⅓