Question

Find the coordinates from the point whose distance from (3,5) is 5 units and from (0,1) is 10 units

Answer 1

The problem can be solved easily using mapping.

Answer 2

The coordinates of the point whose distance from (3,5) is 5 units and from (0,1) is 10 units is ( $2,\frac{11}{3}$ ).

Step-by-step explanation:

We have to find the coordinates of the point whose distance from (3,5) is 5 units and from (0,1) is 10 units.

Let the required coordinated be (x,y)

Suppose on a line segment there are three collinear points where A represents (3,5), B represents (x,y) and C represents (0,1).

The distance between A(3,5) and B(x,y) is given to be 5 units and similarly, the distance between B(x,y) and C(0,1) is given to be 10 units.

Now, we will use the section formula to find the coordinate B(x,y), i.e;

Section formula states that;   $x=\frac{mx_2+nx_1}{m+n}$    and     $y = \frac{my_2+ny_1}{m+n}$

Here, m and n represent the two distance between the coordinates, i.e; m = 5 and n = 10.

Also, ($x_1,y_1$) = A(3,5)   and    ($x_2,y_2$) = C(0,1)

So,  $x=\frac{(5 \times 0)+(10 \times 3)}{5+10}$            and               $y=\frac{(5 \times 1)+(10 \times 5)}{5+10}$

          =  $\frac{30}{15}$  = 2                                             =  $\frac{55}{15} = \frac{11}{3}$

Hence, the required coordinate (x,y) = ( $2,\frac{11}{3}$ ).