Question

On a coordinate plane, a line is drawn from point a to point b. point a is at (9, negative 8) and point b is at (negative 6, 7). what are the x- and y- coordinates of point p on the directed line segment from a to b such that p is two-thirds the length of the line segment from a to b? 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 (2, –1) (4, –3) (–1, 2) (3, –2)

Answer 1

Using proportions, it is found that the coordinates of p in the line segment are given as follows: (-1,2).

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the points are:

• Point a(9, -8).

• Point b(-6, 7).

• Point p(x, y).

p is two-thirds the length of the line segment from a to b, hence:

$p - a = \frac{2}{3}(b - a)$

For the x-coordinate, we have that:

$x - 9 = \frac{2}{3}(-6 - 9)$

x - 9 = -10

x = -1

For the y-coordinate, we have that:

$y + 8 = \frac{2}{3}(7 - (-8))$

y + 8 = 10

y = 2.

The coordinates of p are (-1,2).

More can be learned about proportions at brainly.com/question/24372153

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