Question

(GEOMETRY HELP PLS) What are the x- and y- coordinates of point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B?
(2, –1)

(4, –3)

(–1, 2)

(3, –2)

Answer 1

Coordinate of P is (–1, 2)

Answer 2

The x- and y- coordinates of point P on the directed line segment from A to B is $\left({3,-2}\right)$

Further explanation:

Given:

The options of the point P are as follows.

a.$\left( {2,1}\right)$

b.$\left({4,-3}\right)$

c.$\left({-1,2}\right)$

d.$\left( {3,-2}\right)$

Explanation:

The x-coordinate and y- coordinate of point P on the directed line segment from A to B such that P is $\dfrac{2}{3}$ the length of the line segment from A to B.

The given ratio is $\dfrac{2}{3}.$

The line intersect the points that are $\left( {-6,7}\right)$ and $\left( {9,-8}\right).$

The slope of the line can be obtained as follows.

$\begin{aligned}m&=\frac{{ - 8 - 7}}{{9 + 6}}\\&=\frac{{ - 15}}{{15}}\\&= - 1\\\end{aligned}$

They-coordinate point P can obtain as follows,

$\begin{aligned}y- {\text{coordinate}}&= \frac{2}{3}\left( {{y_2} - {y_1}} \right)\\&= \frac{2}{3}\left( { - 15}\right)\\&= - 10\\\end{aligned}$

Now start from point A and move point 10 units in upward direction.

The x-coordinate point P can obtain as follows,

$\begin{aligned}x - {\text{coordinate}}&=\frac{2}{3}\left( {{x_2} - {x_1}} \right)\\&=\frac{2}{3}\left( {15}\right)\\&= 10\\\end{aligned}$

Now start from point A and move point 10 units in left direction.

The x- and y- coordinates of point P on the directed line segment from A to B is $\left({ - 1,2}\right).$

Option (a) is not correct as the coordinates of point P is $\left( { - 1,2}\right).$

Option (b) is not correct as the coordinates of point P is $\left( { - 1,2}\right).$

Option (c) is correct as the coordinates of point P is $\left({ - 1,2}\right).$

Option (d) is not correct as the coordinates of point P is $\left( { - 1,2}\right).$

Hence, $\boxed{{\text{Option (c)}}}$ is correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear inequalities

Keywords: numbers, slope, slope intercept, inequality, equation, linear equation, shaded region, y-intercept, graph, representation, origin, perpendicular, x-intercept 6.