Question

On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80). What are the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J? x = (StartFraction m Over m n EndFraction) (x 2 minus x 1) x 1 y = (StartFraction m Over m n EndFraction) (y 2 minus y 1) y 1 (40, 96) (85, 105) (80, 104) (96, 72).

Answer 1

The x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J is  (85, 105).

Given

On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80).

Coordinates

The coordinates point any point can be found by using the following formula.

$\rm X=\dfrac{m}{m+n}(x_2-x_1)+x_1\\\\ Y=\dfrac{m}{m+n}(y_2-y_1)+y_1$

The x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J is;

$\rm X=\dfrac{m}{m+n}(x_2-x_1)+x_1\\\\ X = \dfrac{3}{3+5}(-40-160)+160\\\\ X = 3 \times (-25)+160\\\\\X = -75+160\\\\ X = 85\\\\\ Y=\dfrac{m}{m+n}(y_2-y_1)+y_1\\\\ Y=\dfrac{3}{3+5}(80-120)+120\\\\Y =- 3\times 5 +`120\\\\Y=-15+120\\\\Y=105$

Hence, the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J is  (85, 105).

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