Question

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

Answer 1

The coordinates of C are (8,2)

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=(3)/(4)(x_B-x_A)`

Adding xA:

`\displaystyle x=(3)/(4)(x_B-x_A)+x_A`

`\displaystyle x=(3x_B+x_A)/(4)`

Similarily:

`\displaystyle y=(3y_B+y_A)/(4)`

Calculating:

`\displaystyle x=(3(12)-4)/(4)`

x = 8

`\displaystyle y=(3(5)-7)/(4)`

y = 2

The coordinates of C are (8,2)