Prove that the diagonals of a rectangle ABCD with vertices A(2, −1), B(5, −1), C(5, 6) and D(2, 6) are
Question:
Prove that the diagonals of a rectangle ABCD with vertices A(2, −1), B(5, −1), C(5, 6) and D(2, 6) are
equal and bisect each other.
Solution:
The vertices of the rectangle ABCD are A(2, −1), B(5, −1), C(5, 6) and D(2, 6). Now
Coordinates of midpoint of $A C=\left(\frac{2+5}{2}, \frac{-1+6}{2}\right)=\left(\frac{7}{2}, \frac{5}{2}\right)$
Coordinates of midpoint of $B D=\left(\frac{5+2}{2}, \frac{-1+6}{2}\right)=\left(\frac{7}{2}, \frac{5}{2}\right)$
Since, the midpoints of AC and BD coincide, therefore the diagonals of rectangle ABCD bisect each other.
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