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Write the equations of the lines that form the four sides of the right trapezoid with vertices at (−13, 7), (−13, −2), (4, −2), and (13, 7). line passing through (−13, 7) and (−13, −2) line passing through (−13, −2) and (4, −2) line passing through (4, −2) and (13, 7) line passing through (13, 7) and (−13, 7)

Sagot :

sqdancefan

Answer:

  • through (−13, 7) and (−13, −2): x = -13
  • through (−13, −2) and (4, −2): y = -2
  • through (4, −2) and (13, 7): y = x -6
  • through (13, 7) and (−13, 7): y = 7

Step-by-step explanation:

You want the equations of the lines through successive pairs of the points (-13, 7), (-13, -2), (4, -2), and (13, 7).

Lines

When the points have the same x-coordinate, the line is a vertical line with equation x = c, where c is the value of that x-coordinate.

Line AB has equation x = -13.

When the points have the same y-coordinate, the line is a horizontal line with equation y = c, where c is the value of that y-coordinate.

Line BC has equation y = -2.

Line DA has equation y = 7.

When the points have different x- and y-coordinates, the line will have some slope and y-intercept. We can find the slope m and the y-intercept b from the equations ...

  [tex]m=\dfrac{y_2-y_1}{x_2-x_1}\qquad b=y_1-m\cdot x_1[/tex]

For (x1, y1) = (4, -2) and (x2, y2) = (13, 7), we have ...

  [tex]m=\dfrac{7-(-2)}{13-4}=\dfrac{9}{9}=1\qquad b=-2-1(4)=-6\\\\\\y=mx+b\qquad\text{the slope-intercept equation for a line}\\\\\boxed{y=x-6}[/tex]

Line CD has equation y = x -6.

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