Lydia is trying to prove that a quadrilateral in a coordinate plane is a square. First, she uses the slope formula to prove that there are two pairs of parallel sides. Next, she uses the distance formula to prove that all sides are equal. What additional step must Lydia perform before reaching a conclusion that the quadrilateral is a square?
A. Use the distance formula to prove that the diagonals of the quadrilateral are not equal.
B. Use the slope formula to prove that four right angles exist as a result of perpendicular sides.
C. Use the midpoint formula to prove that the diagonals of the quadrilateral do not bisect each other.
D. Use the Pythagorean Theorem to prove that the diagonals of the quadrilateral are twice the length of each side.
Lydia is trying to prove that a quadrilateral in a coordinate plane is a square. First, she uses the slope formula to prove that there are two pairs of parallel sides. Next, she uses the distance formula to prove that all sides are equal. What additional step must Lydia perform before reaching a conclusion that the quadrilateral is a square?
Share
The correct answer is B. Use the slope formula to prove that four right angles exist as a result of perpendicular sides.
Explanation: To conclude that a quadrilateral is a square, Lydia needs to show that not only are there two pairs of parallel sides and all sides of equal length, but also that the angles formed by the sides are right angles (90 degrees). This can be achieved by establishing that the adjacent sides are perpendicular to each other, which can be done using the slope formula. If the slopes of two adjacent sides are negative reciprocals of each other, it confirms that the sides meet at right angles.