Question

Show that A(-3, 2), B (-5, -5), C (2, -3) and D(4, 4) are the vertices of a rhombus.

Answer 1

Step-by-step explanation:

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Answer 2

ABCD is a rhombus.

Step-by-step explanation:

Given: A(-3, 2), B (-5, -5), C (2, -3) and D(4, 4)

Solution:

If ABCD is a rhombus, then all sides will be equal.

d(A, B) = √ (x2 − x1)² + (y2 − y1)² = √(-5+3)² + (-5-2)² = √ 4 +49  = √53

d(B, C) = √ (2+5)² + (-3+5)² = √ 49 + 4 = √53

d(C, D) = √ (4-2)² + (4+3)² = √4 + 49 = √53

d(D, A) = √ (4+3)² + (4-2)² = √49 + 4 = √53

We find that all sides are equal. So ABCD is a rhombus.