Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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.

View image sqdancefan
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.