Answer to Question #139555 in Geometry for Kaiyah

Question

What are the coordinates of the point 2/5 of the way from h to e on the grid

Answer 1

let H coordinates be ($x$₁,y₁)

let E coordinates be ($x$₂,y₂)

 lets find the coordinates of the point 2/5 of the way from h to e on the grid

A ($x$ , y)

using section formula

$x$ = $x$₁ + $\frac{a}{a+b}$ ($x$₂ - $x$₁) and y = y₁ + $\frac{a}{a+b}$ (y₂ - y₁)

a=2 and b=5

$x$ = $x$₁ + $\frac{2}{2+5}$ ($x$₂ - $x$₁) and y = y₁ + $\frac{2}{2+5}$ (y₂ - y₁)

$x$ = $x$₁ + $\frac{2(x_2-x_1)}{7}$ and y =y₁ + $\frac{2(y_2-y_1)}{7}$

$x$ = $x$₁ + $\frac{2x_2-2x_1}{7}$ and y = y₁ + $\frac{2y_2-2y_1}{7}$

$x$ = $\frac{7x_1+2x_2-2x_!}{7}$ and y = $\frac{7y_1+2y_2-2y_1}{7}$

$x$ = $\frac{5x_1+2y_2}{7}$ and y = $\frac{5y_1+2y_2}{7}$

these are the new coordinates

A( $\frac{5x_1+2x_2}{7}$ , $\frac{5y_1+2y_2}{7}$ )