Question

Given CH with C(2, 1) and H(-2,-15), find
the coordinates of E if E divides CH three
fourths of the way from C to H.

Answer 1

The coordinate of E will be (1, -3) if the coordinates of E if E divides CH three -fourths of the way from C to H

Midpoint of a line is a point that divides a line into two equal parts.

If the line is divided in the ratio a:b, then the midpoint formula will be expressed as:

$M(X,Y) =(\frac{ax_1+bx_2}{a+b}, \frac{ay_1+by_2}{a+b})$

Given the coordinate points, C(2, 1) and H(-2, 15) divided in the ratio of 3:4

$X = \frac{3(2)+1(-2)}{3+1}\\X= \frac{6-2}{4}\\X=\frac{4}{4}\\X = 1$

Get the coordinates Y:

$Y = \frac{3(1)+1(-15)}{3+1}\\Y= \frac{3-15}{7}\\Y=\frac{-12}{4}\\Y= -3$

This shows that the coordinate of E will be (1, -3)

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