Question

The points \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) divide the line segment joining the points \(\mathrm{P}(-3, 8)\) and \(\mathrm{Q}(9, -4)\) into four equal parts. If A is nearest to P, then the coordinates of A are ______.

Options

• (–3, 5)

• (0, 5)

• (3, 5)

• (6, –1)

Answer 1

The points \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) divide the line segment joining the points \(\mathrm{P}(-3, 8)\) and \(\mathrm{Q}(9, -4)\) into four equal parts. If A is nearest to P, then the coordinates of A are (0, 5).

Explanation:

A is \(\frac{1}{4}\) of the way from P to Q, so it divides PQ in the ratio 1 : 3:

$$A = \left(\frac{1 \times 9 + 3 \times (-3)}{4}, \frac{1 \times (-4) + 3 \times 8}{4}\right) = (0,5)$$