Question

throu 4. (h) incli Use the point-slope form to find the equation of each alti a triangle is the perpendicular drawn from any vertex to (a) A(1,-2), B(3,4), C(-2,6)

Answer 1

The graph below shows the triangle ABC

We use points C(-2,6) and B(3,4) to find the slope of CB

`m=(y_2-y_1)/(x_2-x_1)=(4-6)/(3-(-2))=(-2)/(3+2)=-(2)/(5)`

Now, we find the perpendicular slope to CB.

`\begin{gathered} m\cdot m_1=-1 \\ m\cdot(-(2)/(5))=-1 \\ m=(5)/(2) \end{gathered}`

The altitude has to pass through point A(1, -2). Let's use the point-slope formula to find the equation

`\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=(5)/(2)(x-1) \\ y+2=(5)/(2)x-(5)/(2) \\ y=(5)/(2)x-(5)/(2)-2 \\ y=(5)/(2)x+(-5-4)/(2) \\ y=(5)/(2)x-(9)/(2) \end{gathered}`

Hence, the equation of the altitude is

`y=(5)/(2)x-(9)/(2)`

This altitude is perpendicular to the side CB.