Question

The points A(9, 0), B(9, –6), C(–9, 0) and D(–9, 6) are the vertices of a ______.

विकल्प

• Square

• Rectangle

• Parallelogram

• Trapezium

Answer 1

The points A(9, 0), B(9, –6), C(–9, 0) and D(–9, 6) are the vertices of a parallelogram.

Explanation:

Given points: A(9, 0), B(9, −6), C(−9, 0), D(−9, 6)

To identify the quadrilateral, we check whether opposite sides are parallel.

Step 1: Check slopes of AB and CD:

Slope of AB: A(9, 0), B(9, −6)

Slope = `(-6-0)/(9-9)`

= `(-6)/0` = Undefined

Slope of CD: C(−9, 0), D(−9, 6)

Slope = `(6 - 0)/(-9 - (-9))`

= `6/0` = Undefined

Since both slopes are undefined.

AB || CD

Step 2: Check slopes of BC and AD:

Slope of BC: B(9, −6), C(−9, 0)

Slope = `(0 - (-6))/(-9 - 9)`

= `6/(-18)`

= `-1/3`

Slope of AD: A(9, 0), D(−9, 6)

Slope = `(6 - 0)/(-9-9)`

= `6/-18`

= `-1/3`

Since slopes are equal.

BC || AD

Conclusion: Both pairs of opposite sides are parallel.

AB || CD and BC || AD

A quadrilateral with both pairs of opposite sides parallel is a parallelogram.