Question

I’m a computer graphics design program, Mario created a segment with endpoints at ( 1, 5) and ( 7, 3). He then reflected the segment about a vertical line through the segment’s own midpoint. WHAT ARE THE COORDINATES OF THE ENDPOINTS OF THE NEW SEGMENTS?

A. (5, 1) and (3, 7)
B (7, 5) and (1, 3)
C. (7, 3) and (1, 5)
D. (5, 1) and (7, 3)

Answer 1

B (7, 5) and (1, 3)

Explanation:

the other answer is right about finding the midpoint :

((x1 + x2)/2, (y1 + y2)/2) = ((1+7)/2, (5+3)/2) =

= (8/2, 8/2) = (4, 4)

now, there is a vertical line through this point, and the original line segment is reflected across this vertical line.

reflections across vertical lines keep the y-values unchanged.

and the x distance of the original point to the midpoint is the same as the x distance of the reflected point to the midpoint.

after all, a reflection means a mirroring.

so, the mirror points are

(..., 5) and (..., 3)

about the x coordinates of distances:

1 to 4 = 3

4 to mirrored point = 3, 4 + 3 = 7.

7 to 4 = 3

4 to mirrored point = 3, 4 - 3 = 1.

so, the points are

(7, 5) and (1, 3)