Question

Prove that the following four points will form a rectangle when connected in order

Answer 1

Answer:

Step-by-step explanation:

If the diagonals of the rectangle are congruent,

AC = BD

By using formula to calculate the distance between two points,

Distance between two points = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Distance between A(0, -3) and C(2, 8),

AC = $\sqrt{(8+3)^2+(2-0)^2}$

     = $\sqrt{125}$

     = $5\sqrt{5}$

Similarly, distance between two points B(-4, 0) and D(6, 5),

BD = $\sqrt{(5-0)^2+(6+4)^2}$

     = $\sqrt{125}$

     = $5\sqrt{5}$

Therefore, both the diagonals are congruent.

Hence, given quadrilateral ABCD is a rectangle.