Answer:
The points that are 17 units from P(-97,2) are:
(-105,-13) and (-105,17)
Step-by-step explanation:
Distance between two points
The distance between points A(x,y) B(w,z) can be calculated with the formula:
[tex]d=\sqrt{(w-x)^2+(z-y)^2}[/tex]
One point is (-105,y) and the other is (-97,2). Computing the distance between them:
[tex]d=\sqrt{(-97-(-105))^2+(2-y)^2}=\sqrt{8^2+(2-y)^2}=\sqrt{64+(2-y)^2}[/tex]
This distance is 17, thus:
[tex]\sqrt{64+(2-y)^2}=17[/tex]
Squaring on both sides:
[tex]64+(2-y)^2=289[/tex]
Operating:
[tex](2-y)^2=289-64=225[/tex]
Taking the square root:
[tex](2-y)=\pm 15[/tex]
There are two possible solutions:
[tex]2-y=15\Rightarrow y=-13[/tex]
[tex]2-y=-15\Rightarrow y=17[/tex]
The points that are 17 units from P(-97,2) are:
(-105,-13) and (-105,17)
