Three vertices of a rectangle are A(−5,3), B(2,3), and C(2,7). Find the coordinates of D to construct the rectangle ABCD.(1 point)
To find the coordinates of point D, we need to find the point that is diagonally opposite to point C.
Since the opposite sides of a rectangle are equal in length, we know that the length of AB is equal to the length of DC, and the length of AC is equal to the length of BD.
The coordinate of D can be found using the following steps:
1. Determine the length of AB:
AB = distance between points A and B
= √((x2 - x1)^2 + (y2 - y1)^2)
= √((2 - (-5))^2 + (3 - 3)^2)
= √(7^2 + 0^2)
= √49
= 7
2. Determine the length of AC:
AC = distance between points A and C
= √((x2 - x1)^2 + (y2 - y1)^2)
= √((2 - (-5))^2 + (7 - 3)^2)
= √(7^2 + 4^2)
= √(49 + 16)
= √65
3. Since AB = DC, the length of DC is also 7.
Since AC = BD, the length of BD is also √65.
4. Starting from point C(2, 7), we can move 7 units to the left to find point D.
D(-5, 7)
Therefore, the coordinates of point D are (-5, 7).