Question

We are reviewing a module and I don't remember how to do it.

Answer 1

The coordinate of point X which is 5/6 of the distance between P and Q is 5/11

Here, we want to calculate the coordinates of point X which is 5/6 of the distance between P and Q

Mathematically, we can use the internal division formula.

In this case, the coordinates of y is 0 in all cases

So the coordinates of P is (-5,0) while the coordinates of Q is (7,0)

Now, the coordinates of X divides the line PQ in the ratio 5 to 6

Using the internal divison formula, we have;

`(x,y)\text{ = }\frac{mx_2+nx_1}{m+\text{ n}},\text{ }\frac{my_2+ny_1}{m+\text{ n}}`

In this case however, we are going to focus on the x-axis part of the question since the values of y at all points is 0

m , n are the division values which are 5 and 6 respectively in this case

x2 is 7 while x1 is -5

Substituting all of these, we have;

`\begin{gathered} (x,y)\text{ = }\frac{5(7)\text{ + 6(-5)}}{11},\text{ 0} \\ \\ (x,y)\text{ = }(35-30)/(11),\text{ 0} \\ (x,y)\text{ = }(5)/(11),\text{ 0} \end{gathered}`

So the coordinate of point X which is 5/6 of the distance between P and Q is 5/11