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SOVA2 [1]
3 years ago
12

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

Mathematics
1 answer:
Lemur [1.5K]3 years ago
8 0

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.

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