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?

Answer 1

Talia must calculate the slopes of the diagonals of a square using coordinates and show that the product of these slopes is -1; this confirms that the diagonals are perpendicular to each other.

Step-by-step explanation:

To show that the diagonals of a square are perpendicular, Talia should:

1. Assign coordinates to each vertex of the square, ensuring that the sides are parallel to the coordinate axes.
2. Calculate the slopes of the two diagonals.
3. Show that the product of these slopes is -1, which indicates that the diagonals are perpendicular to each other because the slope of a line perpendicular to another with a slope of m is -1/m.

By doing this, Talia will have used the coordinate geometry method to prove that the diagonals of the square intersect at perpendicular angles, forming a 90° angle between each other.