Question

Solve to find all points (4, y) that are 10 units from the point (–2, –1).

Answer 1

Given:

Distance between two points (4,y) and (-2,-1) is 10 units.

To Find:

Find the value of y and coordinate of points.

Step-by-step explanation:

• In this given problem two points are given (4,y) and B(-2,-1) and the distance between these points is 10 units.
• Here we will use the distance formula to find the coordinate of the point. The distance formula states that the distance between these two points can be found by subtracting the coordinates.

• Distance between these two(4,y) and (-2,-1) points is 10 units.

     

        $Distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

         $x_1=-2, y_1=-1$

         $x_2=4, y_2=y$

         $10=\sqrt{(4+2)^2+(y+1)^2}$

         $10=\sqrt{(6)^2+(y^2+1+2y)}$

         $10= \sqrt{36+y^2+1+2y}$

         $10=\sqrt{y^2+2y+37}$

         On squaring both sides

         $100=y^2+2y+37$

         $y^2+2y+37-100$

          $y^2+2y-63=0$

          $y^2+9y-7y-63$

          $y(y+9)-7(y+9)$

          $(y-7)(y+9)$

           $y=7,-9$

So, the value of y is 7 or -9 and the point can be (4,7) or (4,-9).