Question

What is the area of a parallelogram whose vertices are A(-12, 2) B(6, 2) C(-2, -3) and D(-20, -3) ?

Answer 1

The area of the parallelogram ABCD is 90 units²

Step-by-step explanation:

Let us revise some rules

• Area of parallelogram is $A=B_{1}*H_{1}=B_{2}*H_{2}$
• The line is horizontal if the y-coordinates of the points lie on it are equal
• The length of the horizontal segment whose end points are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $(x_{2}-x_{1})$

• The line is vertical if the x-coordinates of the point lie on it are equal

• The length of the vertical segment whose end points are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $(y_{2}-y_{1})$

Look to the attached figure

∵ ABCD is a parallelogram whose vertices are

   A (-12 , 2) ,  B (6 , 2) , C (-2 , -3) and D (-20 , -3)

∵ The y-coordinates of points A and B are equal

∴ AB is a horizontal segment

∵ The y-coordinates of points C and D are equal

∴ CD is a horizontal segment

∴ AB // CD

∵ AB = 6 - (-12) = 6 + 12 = 18 units

∵ CD = -2 - (-20) = -2 + 20 = 18 units

∴ $B_{1}$ = 18 units

∵ The height of the bases AB and CD is AE

∵ AE is a vertical line

∴ The length of AE is the difference between the y-coordinates of

   points A and D

∴ AE = 2 - (-3) = 2 + 3 = 5 units

∴ $H_{1}$ = 5 units

∵ $A=B_{1}*H_{1}$

∴ A = 18 × 5 = 90 unit²

The area of the parallelogram ABCD is 90 units²

Learn more:

You can learn more about parallelograms in brainly.com/question/4459688

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