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.

Answer 1

Solution:- Given vertices of triangle are A(−3, 0), B(4, 5), C(0, −4)

With the help of given points we construct triangle ABC.(see figure)

To find coordinates of intersection of side AB with y-axis,

we need to find the equation of line AB with coordinates A(−3, 0)  and B(4, 5)

Here slope of AB m=$\frac{y_2-y_1}{x_2-x_1} =\frac{5-0}{4+3} =\frac{5}{7}$

We know that the equation of line with slope m is

$(y-y_1)=m(x-x_1)$

$\Rightarrow(y-0)=\frac{5}{7}(x+3)\\\Rightarrow\ y=\frac{5}{7}(x+3)$.......(1)

For intersection with y axis the point of intersection would be (0,a) from the figure

so putting x=0 in (1) we get,

$y=\frac{5}{7}(0+3)=\frac{15}{7} =2.14$

So the coordinates of intersection of side AB with the y-axis would be =(0,2.14)