Question

The points A(5, –1, 1); B(7, –4, 7); C(1, –6, 10) and D(–1, –3, 4) are vertices of a ______.

Options

• square

• rhombus

• rectangle

• trapezium

Answer 1

The points A(5, –1, 1); B(7, –4, 7); C(1, –6, 10) and D(–1, –3, 4) are vertices of a rhombus.

Explanation:

AB = `sqrt(4 + 9 + 36)` = 7

BC = 7

CD = 7

DA = 7

AC = `sqrt(16 + 25 + 81)`

= `sqrt(122)`

BD = `sqrt(64 + 1 + 9)`

= `sqrt(74)` rhombus.