MATH SOLVE

4 months ago

Q:
# What is the area of a parallelogram whose vertices are A(-12, 2) B(6, 2) C(-2, -3) and D(-20, -3) ?Please help my I’m trying to get my grades up

Accepted Solution

A:

The area of the parallelogram ABCD is 90 units²Step-by-step explanation:Let us revise some rulesArea of parallelogram is [tex]A=B_{1}*H_{1}=B_{2}*H_{2}[/tex]The line is horizontal if the y-coordinates of the points lie on it are equalThe length of the horizontal segment whose end points are [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](x_{2}-x_{1})[/tex]The line is vertical if the x-coordinates of the point lie on it are equalThe length of the vertical segment whose end points are [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](y_{2}-y_{1})[/tex]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∴ [tex]B_{1}[/tex] = 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∴ [tex]H_{1}[/tex] = 5 units∵ [tex]A=B_{1}*H_{1}[/tex]∴ A = 18 × 5 = 90 unit²The area of the parallelogram ABCD is 90 units²Learn more:You can learn more about parallelograms in brainly.com/question/4459688#LearnwithBrainly