Question

What is the area of a parallelogram whose vertices are (-4,9), (11,9), (5,-1) and (-10,-1)

Answer 1

The area of the parallelogram whose vertices are (-4 , 9), (11 , 9), (5 , -1)

and (-10 ,-1) is 150 units²

Step-by-step explanation:

Let us revise some important facts:

1. Horizontal lines passe through points have same y-coordinates

2. The length of a horizontal segment is the difference between

    the x-coordinates of its end-points

3. vertical lines passe through points have same x-coordinates

4. The length of a vertical segment is the difference between

    the y-coordinates of its end-points

In the parallelogram whose vertices are

(-4 , 9), (11 , 9), (5 , -1) and (-10 ,-1)

∵ The vertices (-4 , 9) and (11 , 9) have same y-coordinates

∴ The side whose joining them is a horizontal side

∴ Its length = 11 - (-4) = 11 + 4 = 15 units

∵ The vertices (5 , -1) and (-10 , -1) have same y-coordinates

∴ The side whose joining them is a horizontal side

∴ Its length = 5 - (-10) = 5 + 10 = 15 units

∴ The two horizontal sides are parallel and equal

∵ The area of a parallelogram = $base_{1}$ × $height_{1}$

∵ The perpendicular distance between two parallel horizontal

   sides is the difference between their y-coordinates

∵ The y-coordinate of the 1st horizontal side = 9

∵ The y-coordinate of the 2nd horizontal side = -1

∴ The vertical distance between the parallel sides = 9 - (-1) = 9 + 1

∴ The vertical distance between the parallel sides = 10 units

∵ $base_{1}$ = 15 units

∵ $height_{1}$ = 10 units

∴ The area of the parallelogram = 15 × 10 = 150 units²

The area of the parallelogram whose vertices are (-4 , 9), (11 , 9),

(5 , -1) and (-10 ,-1) is 150 units²

Learn more:

You can learn more about area of parallelograms in brainly.com/question/6779145

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