Question

discuss how you can find the coordinate of a point located other fractional distances from a to b (or from b to a.) for example, locate a point three-fourths of the distance from a to b. what kind of calculation is involved?

Answer 1

the coordinates of the point three-fourths of the distance from A to B is (-1/4, 3 1/4)

See explanation below

Step-by-step 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:

`For\text{ the x coordinate : }x_1+(3)/(4)(\Delta x)`
`For\text{ the y coordinate: }y_1+(3)/(4)(\Delta y)`
`\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 + }(3)/(4)(-3)\text{ = 2 + }(-9)/(4) \\ =\text{ }\frac{8\text{ - (+9)}}{4}=(8-9)/(4) \\ x\text{ coordinate }=\text{ -1/4} \end{gathered}`
`\begin{gathered} \Delta y=y_2-y_1\text{ = 4-1} \\ \Delta y\text{ = 3} \\ y\text{ coordinate = }1\text{ + }(3)/(4)(3)\text{ =1 + }(9)/(4)\text{ } \\ =\text{ }\frac{4\text{ + 9}}{4}=(13)/(4) \\ y\text{ coordinate =}3(1)/(4) \end{gathered}`

Hence, the coordinates of the point three-fourths of the distance from A to B is (-1/4, 3 1/4)