EXPLANATION
Given the pairs: A(-7,3) and B(5,8)
In order to calculate the distance between points, we need to apply the following formula:
[tex]dis\tan ce=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Considering:
(x1,y1) = (-7,3) and (x2,y2) = (5,8), replacing terms, will give us:
[tex]\text{distance = }\sqrt[]{(8-3)^2+(5-(-7))^2}[/tex][tex]\text{distance = }\sqrt[]{5^2+12^2}[/tex]
Simplifying:
[tex]dis\tan ce=\sqrt[]{169}=13[/tex]
(b) The length of segment Ab is equal to 13.
Now, we need to find the length of the segment A'B'.
As we can see, A'B' is a reflection over the line y=x
So, the transformation will have the following coordinates:
A'=(x'1,y'1) =(3,-7) (x'2,y'2) = (8,5)
Given that the image is a reflection of the preimage, the distance between pre-images equals the distance between their images. Reflections preserve distance. The distance between A' and B' will be the same that the distance between A and B. So distance will be equal.
