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? Responses Show that SQ = PR StartFragment, Show that SQ = PR, Show that the midpoint of line SQ is the same as the midpoint of line PR. StartFragment, Show that the midpoint of line SQ is the same as the midpoint of line PR., Show that line SQ and line PR intersect at (a/2), a/2) StartFragment, Show that line SQ and line PR intersect at (a/2), a/2 ), Show that the slope of line SQ is 1 and the slope of line PR is -1.

Answer 1

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

Explanation:

To show that the diagonals of a square are perpendicular, Talia should demonstrate that the slope of one diagonal is the negative reciprocal of the slope of the other diagonal. Therefore, the correct sentence is:

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

In a square, the diagonals are perpendicular, which means that their slopes are negative reciprocals of each other. This property is a key characteristic of squares, and it's commonly used to prove their diagonals' perpendicularity.