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)

Coordinates are two integers (Cartesian coordinates) or a letter and a number that point to a specific place on a grid known as a coordinate plane.
A coordinate plane has four quadrants and two axes: x (horizontal) and y (vertical) (vertical).

To find What are the x- and y- coordinates of point p on the directed line segment from K to J:

It can be seen from the figure the coordinates of K and J:

K ( 160 ,120) and J (-40 , 80)

The coordinates of P can be determined as:

[tex]x=\frac{m}{m+n} (x_{2}-x_{1})+x_{1} } \\y=\frac{m}{m+n} (y_{2}-y_{1})+y_{1} } \\[/tex]

So, as the P point divides the line into three-fifths of the length,

KP = (3/5)KJ
JP = (2/5) KJ

Which gives the ratio as 3: 2.

m:n = 3:2

x = (3/5) (-40 -160) + (160)
x = 40
y = ( 3/5)(-40) +120
y = 96

Therefore, the coordinate of P is (A) ( 40, 96).

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The complete question is shown below:

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

(A) (40, 96)

(B) (85, 105)

(C) (80, 104)

(D) (96, 72)