Use the following graph and answer the given questions :

(a) From graph,

Coordinates of :

A(4, 8), B(-1, 2), C(6, 2)

Hence, A(4, 8), B(-1, 2), C(6, 2).

(b) Midpoint of AC,

By formula,

Midpoint = $\Big(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\Big)$

Substituting values, we get :

Mid-point of AC = $\Big(\frac{4 + 6}{2}, \frac{8 + 2}{2}\Big)$ = (5, 5).

By formula,

Slope = $\frac{y_2 - y_1}{x_2 - x_1}$

Thus,

Slope of AB = $\frac{8 - 2}{4 - (-1)}$

= $\frac{6}{5}$.

Since, slope of parallel lines are equal, thus slope of required line (m) = $\frac{6}{5}$.

By point-slope form,

Equation : y - y₁ = m(x - x₁)

Equation of line parallel to AB and passing through mid-point of AC is given by,

⇒ y - 5 = $\frac{6}{5}(x - 5)$

⇒ 5(y - 5) = 6(x - 5)

⇒ 5y - 25 = 6x - 30

⇒ 5y - 25 + 30 = 6x - 30

⇒ 5y - 5 = 6x

⇒ 6x - 5y - 5 = 0.

Hence, equation of required line = 6x - 5y - 5 = 0.