Question

talia is writing a coordinate proof to show that the diagonals of a square are perpendicular. she begins by assigning coordinates to the vertices of a square as shown. which sentence describes what talia should do to show that the diagonals of the square are perpendicular? p(0, a) q(a, a) s(0, 0) r(a, 0) show that the slope of the line sq is 1 and the slope of pr is -1 show that sq=pr show that the midpoint of the line sq is the same as the midpoint of the line pr show that the line sq and line pr intersect at (a/2,a/2)

Explanation:

To determine if two lines are perpendicular, we use the property that the product of their slopes is \(-1\) (or one slope is the negative reciprocal of the other). Let's analyze each option:

• Option 1: If the slope of \(SQ\) is \(1\) and the slope of \(PR\) is \(-1\), then the product of the slopes is \(1\times(-1) = -1\), which satisfies the perpendicular slope condition.
• Option 2: Showing \(SQ = PR\) proves the diagonals are equal, not perpendicular.
• Option 3: Showing the midpoints are the same proves the diagonals bisect each other, not perpendicular.
• Option 4: Showing the intersection point does not prove perpendicularity.

So, the correct approach is to show the slopes multiply to \(-1\) (or are negative reciprocals), which matches the first option.

Answer:

A. Show that the slope of the line SQ is 1 and the slope of PR is -1