Answer :
the coordinates of the point three-fourths of the distance from A to B is (-1/4, 3 1/4)
See explanation below
Explanation:
We will be using a problem on it to explain
Example: Find the coordinates of the point which is three fourth of the way from (2,1) t0 B(-1, 4)
There different method to approach such questions.
We will apply the formula below:
[tex]For\text{ the x coordinate : }x_1+\frac{3}{4}(\Delta x)[/tex][tex]For\text{ the y coordinate: }y_1+\frac{3}{4}(\Delta y)[/tex][tex]\begin{gathered} x_{1\text{ }}=2,y_1=\text{ 1, }x_{2\text{ }}=-1,y_2=\text{ 4} \\ \Delta x\text{ = }x_2-x_1\text{ = }-1\text{ -2 } \\ \Delta x\text{ = -3} \\ x\text{ coordinate = 2 + }\frac{3}{4}(-3)\text{ = 2 + }\frac{-9}{4} \\ =\text{ }\frac{8\text{ - (+9)}}{4}=\frac{8-9}{4} \\ x\text{ coordinate }=\text{ -1/4} \end{gathered}[/tex][tex]\begin{gathered} \Delta y=y_2-y_1\text{ = 4-1} \\ \Delta y\text{ = 3} \\ y\text{ coordinate = }1\text{ + }\frac{3}{4}(3)\text{ =1 + }\frac{9}{4}\text{ } \\ =\text{ }\frac{4\text{ + 9}}{4}=\frac{13}{4} \\ y\text{ coordinate =}3\frac{1}{4} \end{gathered}[/tex]Hence, the coordinates of the point three-fourths of the distance from A to B is (-1/4, 3 1/4)