Question

Segment AB has endpoints at A(-7,2) and b(9,-6). Point P lies on AB such that AP:BP=3:1

Answer 1

The coordinates of the point P which divides the line segment AB made by the points A(-7,2) and B(9,-6) is  (x,y) = (5,-4)

What is the coordinate of the point which divides a line segment in a specified ratio?

Suppose that there is a line segment $\overline{AB}$such that a point P(x,y) lying on that line segment $\overline{AB}$ divides the line segment  $\overline{AB}$ in m:n, then, the coordinates of the point P is given by:

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

where we have:

• the coordinate of A is $(x_1, y_1)$
• and the coordinate of B is $(x_2, y_2)$

We're given that:

• Coordinate of A is $(x_1, y_1)$ = (-7,2)
• Coordinate of B is $(x_2, y_2)$ = (9.-6)
• The point P lies on AB such that AP:BP=3:1 (so m = 3, and n = 1)

Let the coordinate of P be (x,y), then we get the values of x and y as:

$(x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)\\\\(x,y) = \left( \dfrac{3(9) + 1(-7)}{3+1} , \dfrac{3(-6) + 1(2)}{3+1} \right)\\\\(x,y) = \left( \dfrac{20}{4} , \dfrac{-16}{4} \right) = (5,-4)$

Thus, the coordinates of the point P which divides the line segment AB made by the points A(-7,2) and B(9,-6) is  (x,y) = (5,-4)

Learn more about a point dividing a line segment in a ratio here:

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