Question

Construct the triangle ABC using as coordinates of its vertices points A(−3, 0), B(4, 5), C(0, −4). Find the coordinates of intersection of side AB with the y-axis.
DO NOT GIVE ME THE ANSWER OF (0,2) IT IS WRONG!
Pls graph it and give me another answer 15 points!!!!!!!!!

Answer 1

Plot all points on the coordinate plane and combine these points by lines to get triangle ABC (see attached picture for details).

Write the equation of side AB:

$\dfrac{x-(-3)}{4-(-3)}=\dfrac{y-0}{5-0} ,\\ \\\dfrac{x+3}{7}=\dfrac{y}{5},\\ \\y=\dfrac{5}{7}x+\dfrac{15}{7}.$

To find y-intercept you have to substitute x=0, then:

$y=\dfrac{5}{7}\cdot 0+\dfrac{15}{7}=\dfrac{15}{7}=2\dfrac{1}{7}.$

The point $\left(0,2\dfrac{1}{7} \right)$ is the point where line AB intersects y-axis.