Equation Finder Problem

Question

Line l bisects segment BC of triangle ABC, where A is at (3, -3), B is at (1, 4), and C is at (3, -2). If line l also travels through point A, what is its equation?

A. y=-5x-1

B. y=-2x+4

C. y=-4x+9

D. y=4x-1

E. y=5x+4

Answer 1

If line "l" bisects BC, then it goes through the midpoint. Calculate the midpoint using the midpoint formula:

x_midpoint = (x₁ + x₂)/2 = (1 + 3)/2 = 2

y_midpoint = (y₁ + y₂)/2 = (4 + -2)/2 = 1

So the midpoint is (2, 1)

It also goes through (3, -3)

Use the point-slope form of a line. First calculate the slope (m) using the slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

m = (-3 - 1)/(3 - 2) = -4/1 = -4

The point-slope form is:

y - y₁ = m(x - x₁)

using m = -4 and (x₁, y₁) = (2, 1):

y - 1 = -4(x - 2)

y - 1 = -4x + 8

y = -4x + 9

Answer 2

The midpoint of segment BC is (2,1) (use the midpoint formula).

Now you have two points that the line passes through (2,1) and (3,-3). Calculate the slope of that line using the formula for slope (change in y / change in x).

Now use point-slope formula to find the equation of the line. Finally convert that equation to slope-intercept form to match one of the multiple choice answers.

Check your result here:

desmos.com/calculator/epgj6mehqb