Question

Determine the coordinates of the point $P$ on the line $y=-x+6$ such that $P$ is equidistant from the points $A(10,-10)$ and $O(0,0)$ (that is, so that $PA=PO$). Express your answer as an ordered pair $(a,b)$.

Answer 1

Answer:

P=(3,3)

Step-by-step explanation:

We need to find a point  P in the line $y=-x+6$ such that $PA=P0$ where $A=(10,-10)$

Observe that the coordinates of P are $(x,y)=(x,-x+6)$ because P is in the line.

Then,

$PA=P0\\(x,-x+6)(10,-10)=(x,-x+6)(0,0)\\10x+(-x+6)(-10)=0\\10x+10x-60=0\\20x=60\\x=3$

We reeplace  the value of x in the coordinates of P and obtain the point

$(3,-3+6)=(3,3)=P$