The point P(-4, 1) divides the line segment joining the points A(2, -2) and B in the ratio 3 : 5. Find the point B.

Let the coordinates of B be (x, y).

As the point P(-4, 1) divides the line segment joining the points A (2, -2) and B (x, y) in the ratio 3 : 5, we have

We know that,

Section-formula = $\Big(\dfrac{m$1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big).

Putting values in above equation we get coordinates of P as

$= \Big(\dfrac{3 \times x + 5 \times 2}{3 + 5}, \dfrac{3 \times y + 5 \times (-2)}{3 + 5}\Big) \\[1em] = \Big(\dfrac{3x + 10}{8}, \dfrac{3y - 10}{8}\Big).$

According to question the coordinates of P are (-4, 1) comparing we get,

$\Rightarrow \dfrac{3x + 10}{8} = -4 \text{ and } \dfrac{3y - 10}{8} = 1$
⇒ 3x + 10 = -32 and 3y - 10 = 8
⇒ 3x = -32 - 10 and 3y = 8 + 10
⇒ 3x = -42 and 3y = 18
⇒ x = -14 and y = 6.

∴ B = (x, y) = (-14, 6).

Hence, the coordinates of B are (-14, 6).