Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Triangle ABC is defined by the points A(3,8), B(7,5), and C(2,3).
Create an equation for a line passing through point A and perpendicular to BC.

Sagot :

abidemiokin

The required equation for a line passing through point A and perpendicular to BC is 2y + 5x = 31

First, we need to get the slope of the line perpendicular to BC

  • Given the coordinates B(7,5), and C(2,3)

Get the slope BC:

[tex]m_{BC} = \frac{3-5}{2-7}\\m_{BC}=\frac{-2}{-5}\\m_{BC}=\frac{2}{5}\\[/tex]

The slope of the line perpendicular to BC will be -5/2

The slope of the required line in point-slope form is expressed as;

[tex]y-y_0=m(x-x_0)\\[/tex]

Given the following

m = -5/2

(x0, y0) = (3, 8)

Substitute into the formula:

[tex]y-8=-5/2(x-3)\\2(y-8)=-5(x-3)\\2y - 16=-5x+15\\2y+5x=15+16\\2y+5x=31\\[/tex]

Hence the required equation for a line passing through point A and perpendicular to BC is 2y + 5x = 31

Learn more here: https://brainly.com/question/17119045

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.