Question

10

Answer 1

Answer:

Step-by-step explanation:

The formulas to find the x and y coordinates of E are:

$x=\frac{bx_1+ax_2}{a+b}$  and  $y=\frac{by_1+ay_2}{a+b}$  where x1, x2, y1, and y2 are from the coordinates of A and B, and a = 1 (from the ratio) and b = 2 (from the ratio). Filling in to find x first:

$x=\frac{2(2)+1(-4)}{1+2}=\frac{4-4}{3}=0$  and now for y:

$y=\frac{2(-3)+1(9)}{1+2}=\frac{-6+9}{3}=\frac{3}{3}=1$

The coordinates of E are (0, 1).

Answer 2

Given:

The points are A(2,-3) and B(-4,9).

The point E divides the segment AB in 1:2.

To find:

The coordinates of point E.

Solution:

Section formula: If a point divides a line segment in m:n, then the coordinates of the point is:

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Using the section formula, the coordinates of point E are:

$E=\left(\dfrac{1(-4)+2(2)}{1+2},\dfrac{1(9)+2(-3)}{1+2}\right)$

$E=\left(\dfrac{-4+4)}{3},\dfrac{9-6}{3}\right)$

$E=\left(\dfrac{0)}{3},\dfrac{3}{3}\right)$

$E=\left(0,1\right)$

Therefore, the coordinates of the point E are (0,1).