Question

The diagonals of rectangle KLMN intersect at the point (2, 1). One of the vertices of rectangle KLMN is located at (-4, 5). A 8 6 -5 4 -3 -2 3 -4 5 6 7 8 9 89 Which of the following could be the location of another vertex of this rectangle?​

Answer 1

H (8, -3)

Explanation:

You want a possible vertex of rectangle KLMN if the midpoint of the diagonals is (2, 1) and one of the vertices is (-4, 5).

Rectangle

The diagonals of a rectangle are congruent and bisect each other, so the given point of intersection is the midpoint of the diagonals. If one of the diagonal end points is K = (-4, 5), then the other end of that diagonal is ...

X = (K+M)/2

M = 2X -K = 2(2, 1) -(-4, 5) = (2·2+4, 2·1-5)

M = (8, -3)

Another vertex on the rectangle is (8, -3).

__

Additional comment

Segment KM will be the diameter of the circumcircle of the rectangle. Other possible vertices will lie on that circle. As it happens, none of the offered choices is the same distance from X as point K is.

The attached figure shows the given diagonal and one of an infinite number of possible rectangles KLMN.

The choice of naming the given vertex K is arbitrary.