Question

What are the x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2? 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 (0, 1) (–1, 3) (–2, 5) (1, 0).

Answer 1

The x =0 and y = 1 are coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2.

We have to determine

What are the x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2?

According to the question

A line segment at points A(2, -3) and B (-4, 9).

The x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2 is given by;

$\rm x=\dfrac{m}{(m+n)} [x_2- x_1]+ x_1 \\ \\ y=\dfrac{m}{(m+n)} [y_2- y_1]+ y_1$

Where $\rm x_1 = 2 , \ x_2 =-4, \ y_1 =-3, \ y_2 = 9$

Substitute all the values in the formula;

$\rm x=\dfrac{m}{(m+n)} [x_2- x_1]+ x_1$

$\rm x=\dfrac{1}{(1+2)} [-4-(2)]+ (2)\\\\ x = \dfrac{1}{3} \times (-6) +2 \\ \\ x = -2+2\\ \\ x=0$

$\rm y=\dfrac{m}{(m+n)} [y_2- y_1]+ y_1 \\\\ y=\dfrac{1}{(1+2)} [9-(-3)]+ (-3)\\\\ y = \dfrac{1}{3} \times (12) -3\\ \\ y = 4-3\\ \\ y =1$

Hence, the x =0 and y = 1 are coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2.

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