Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Distance Between Points in the Plane

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

$d=\sqrt{(z-y)^2+(w-x)^2}$

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)