Question

The point 3/4 of the way from A(-4,- 7) to B(12, 5)

Answer 1

Answer:

The coordinates of C are (8,2)

Step-by-step explanation:

We are given the segment from A(-4,-7) to B(12,5) and it's required to find a point C(x,y) that is located at 3/4 of the distance from A to B.

This means that:

$d_{AC}=3/4\cdot d_{AB}$

where dAC is the distance from A to C and dAB is the distance from A to B.

The same proportion of the distances is satisfied by the coordinates of the point C, that is:

$\displaystyle x-x_A=\frac{3}{4}(x_B-x_A)$

Adding xA:

$\displaystyle x=\frac{3}{4}(x_B-x_A)+x_A$

$\displaystyle x=\frac{3x_B+x_A}{4}$

Similarily:

$\displaystyle y=\frac{3y_B+y_A}{4}$

Calculating:

$\displaystyle x=\frac{3(12)-4}{4}$

x = 8

$\displaystyle y=\frac{3(5)-7}{4}$

y = 2

The coordinates of C are (8,2)