Question

construct the triangle DCE using as coordinates of its vertices points D (-4,0) C(0,-2) and E(5,3). Find the coordinates of the intersection of side CE with the x
axis

Answer 1

Given that triangle DCE is constructed using coordinates of its vertices points D (-4,0) C(0,-2) and E(5,3).

Joining C and E, we get a line CE which will intersect x-axis.

We have to find that point of intersection.

Before that we need to find equation of line CE

slope of CE is given by

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{\left(3--2\right)}{5-0}=1$

m=1

Now plug the slope m=1 and any point say (0,-2) into point slope formula

$y-y_1=m\left(x-x_1\right)$

y--2=1(x-0)

y+2=1x

y=1x-2

Hence equation of line CE is y=1x-2

We know that when any line crosses x-axis then y=0

so plug y=0 in above equation

0=1x-2

2=x

Hence side CE crosses x-axis at the intersection point (2,0)