Question

Given: Circle P has a center at (4, -4) Given: (1, 0) is a point on the circle Determine the diameter of circle P? 12 units 10 units 4 units 5 units

Answer 1

where the green point is the center of the circle and red a point

If I draw a line from the center to a point on the circle I will get the radius, so the yellow line is the radius, and I can find it using the formula of distance between two points

$\sqrt[]{(x2-x1)^2+(y2-y1)}^2$

where the points are (4,-4) and (1,0)

so, replacing

$\begin{gathered} \sqrt[]{(4-1)^2+(-4-0)^2} \\ \\ \sqrt[]{3^2+(-4)^2} \\ \\ \sqrt[]{9+16} \\ \\ \sqrt[]{25}=5 \end{gathered}$

so the radius is 5

the diameter is 2r so ,replacing

$2\times5=10$

the diameter is 10 units