The coordinates of the vertices of triangle ABC are A(-2, 1), B(4, -2) and C(1,...

Explanation

Gradient of BC = \(\frac{8 + 2}{1 - 4} = -\frac{10}{3}\)

Gradient of DC = \(\frac{8 - y}{1 - x}\)

BDC is a straight line , so

Gradient of BC = Gradient of DC.

\(\frac{10}{-3} = \frac{8 - y}{1 - x}\)

\(-3(8 - y) = 10(1 - x) \implies 3y - 24 = 10 - 10x\)

\(3y + 10x = 34\)

(b) \(\overrightarrow{BC} = \overrightarrow{OC} - \overrightarrow{OB}\)

= \((i + 8j) - (4i - 2j)\)

= \(-3i + 10j\)

\(|\overrightarrow{BC}| = \sqrt{(-3)^{2} + (10)^{2}}\)

= \(\sqrt{109}\)

Unit vector in the direction of BC = \(\frac{(-3i + 10j)}{\sqrt{109}}\)