The values of x and y are 8 and 0 respectively.
Explanation
As 'p' is located at (0,0) and 'r' is located at (-12,0) , that means both 'p' and 'r' are on the x-axis. So point 'q' will be also on the x-axis , and 'q' is located at (x,y)
So, the value of y will be 0. That means the co ordinate of point 'q' is (x, 0)
Now, using the Distance formula, length of 'pq' [tex]= \sqrt{(x-0)^2 +(0-0)^2}= \sqrt{x^2}= x[/tex]
and length of 'pr' [tex]= \sqrt{(-12-0)^2+(0-0)^2}= \sqrt{144}=12[/tex]
Given that, pq : pr =2/3
So....
[tex]\frac{x}{12} =\frac{2}{3}\\ \\ 3x=24\\ \\ x= \frac{24}{3}=8[/tex]
Thus, the values of x and y are 8 and 0 respectively.
