Use the following graph and answer the given questions :

(a) Write the co-ordinates of points A, B and C.

(b) Find the equation of a line passing through the mid-point of AC and parallel to AB.

(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(\dfrac{x$1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

Substituting values, we get :

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

By formula,

Slope = $\dfrac{y$2 - y1}{x2 - x1}

Thus,

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

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

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

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 = $\dfrac{6}{5}(x - 5)$

⇒ 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.