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:
[tex]d_{AC}=3/4\cdot d_{AB}[/tex]
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:
[tex]\displaystyle x-x_A=\frac{3}{4}(x_B-x_A)[/tex]
Adding xA:
[tex]\displaystyle x=\frac{3}{4}(x_B-x_A)+x_A[/tex]
[tex]\displaystyle x=\frac{3x_B+x_A}{4}[/tex]
Similarily:
[tex]\displaystyle y=\frac{3y_B+y_A}{4}[/tex]
Calculating:
[tex]\displaystyle x=\frac{3(12)-4}{4}[/tex]
x = 8
[tex]\displaystyle y=\frac{3(5)-7}{4}[/tex]
y = 2
The coordinates of C are (8,2)
