Plot the points in the coordinate plane, and then construct perpendicular bisectors of two sides to locate the center of a circle.
Location of the Fourth Tower: (3,4) Equation of the Circle: (x-3)^2+(y-4)^2=25
Practice makes perfect
It is a given that three cell towers are modeled by the three points. We are asked to determine the location of another tower that is equidistant — an equal distance — from all three towers. We must then write an equation of a circle. First, let's plot the given points in the coordinate plane.
Now, let's connect the points to form triangle XYZ.
Next, we will construct the perpendicular bisectors of sides XY and ZY. We will label the point of intersection of these segments as C. This point will be the location of another tower equidistant from all three towers.
The location of the fourth tower is (3,4). Notice that points X,Y, and Z lie on the circle with center C and radius r.
From the graph, we can see that the radius of the circle is 5 units. Let's substitute this value and the center point (3,4) into the standard equation of a circle.
(x-3)^2+(y-4)^2= 5^2 ⇓
(x-3)^2+(y-4)^2=25
