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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)

Respuesta :

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:

[tex]p - a = \frac{2}{3}(b - a)[/tex]

For the x-coordinate, we have that:

[tex]x - 9 = \frac{2}{3}(-6 - 9)[/tex]

x - 9 = -10

x = -1

For the y-coordinate, we have that:

[tex]y + 8 = \frac{2}{3}(7 - (-8))[/tex]

y + 8 = 10

y = 2.

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

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

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Answer: (-1,2)

Step-by-step explanation: took the test, got it right!

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