Question

Find all the points (x,6) that are 10 units from the point P (-17,-2)

Answer 1

The points that are 10 units from P(-17,-2) are (-23,6) and (-11,6)

Explanation:

Distance Between Points in the Plane

Given two points A(x,y) and B(w,z), the distance between them is:

`d=√((z-y)^2+(w-x)^2)`

It can be also expressed as:

`d^2=(z-y)^2+(w-x)^2`

Substituting the values of both points, and knowing the distance is 10:

`10^2=(6-(-2))^2+(x+17)^2`

`100=8^2+(x+17)^2`

Swapping both sides:

`64+(x+17)^2=100`

Moving the constants to the right side:

`(x+17)^2=100-64=36`

Taking the square root:

`x+17=\pm 6`

We get two possible answers:

`x=-17-6=-23`

`x=-17+6=-11`

Thus the points that are 10 units from the point P(-17,-2) are (-23,6) and (-11,6)