Question

Point P is on segment AB such that AP:PB is 4:5. If A has coordinates (4,2), and B has coordinates (22,2), determine and state the coordinates of P.

Answer 1

The coordinates of P are (12, 2).

Solution:

Given data:

$(x_1, y_1)= A (4, 2)$  and $(x_2, y_2)=B(22, 2)$

P(x, y) is the point on the line segment AB.

AP : PB = m : n = 4 : 5.

That is m = 4 and n = 5.

Section formula:

$P(x, y)=\left(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}\right)$

$P(x, y)=\left(\frac{4\times 22 + 5\times 4}{4+5}, \frac{4\times 2 + 5\times 2}{4+5}\right)$

$P(x, y)=\left(\frac{88 + 20}{9}, \frac{8+10}{9}\right)$

$P(x, y)=\left(\frac{108}{9}, \frac{18}{9}\right)$

P(x, y) = (12, 2)

Hence the coordinates of P are (12, 2).