Question

The grid at the right has the segment AB drawn with endpoints at A(-7,3) and B(5,8).(a) Draw the image of segment AB, segment A'B', after a reflections in the line y=x. State the coordinates of A' and B' below.(b) Find the length of segment AB and the length of segment A'B' by using the distance formula. Show your work.(c) Explain why the lengths you found in (b) must be equal.

Answer 1

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:

`dis\tan ce=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}`

Considering:

(x1,y1) = (-7,3) and (x2,y2) = (5,8), replacing terms, will give us:

`\text{distance = }\sqrt[]{(8-3)^2+(5-(-7))^2}`
`\text{distance = }\sqrt[]{5^2+12^2}`

Simplifying:

`dis\tan ce=\sqrt[]{169}=13`

(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.