Question

Find the coordinates of the point 7 10 of the way from A to B.

Answer 1

Explanation:

Answer 2

The coordinates of the point 7/10 of the way from A to B is (30/17,-8/17)

Here, what we simply want to do is to find the coordinates of the point that divide the line in the ratio 7 to 10 (7 ratio 10)

To do this, we are to use the internal division formula as follows

Thus, we have;

`(x,y)\text{ =( }\frac{nx_1+mx_2}{m\text{ + n}},\text{ }\frac{ny_1\text{ + m}y_2}{m+n})`

With respect to the question, we have;

`\begin{gathered} m\text{ = 7} \\ n\text{ = 10} \\ \\ x_1\text{ =-4} \\ x_2\text{ = 10} \\ \\ y_1\text{ = -5} \\ y_2\text{ = 6} \end{gathered}`

Substituting these values into the internal division formula, we have;

`\begin{gathered} (x,y)\text{ = (}\frac{10(-4)\text{ + 7(10)}}{10+7},\text{ }\frac{10(-5)\text{ + 7(6)}}{10+7}) \\ \\ (x,y)\text{ = }(-40+70)/(17),\text{ }(-50+42)/(17) \\ \\ (x,y)\text{ = (}(30)/(17),(-8)/(17)) \end{gathered}`