Question

circle c has its center at (5,0) and a point is on the circle at m(7,4). determine if the point q(12, -3) is also on the circle. drag and drop the answers to the boxes to complete the sentences. use the equation (5 - 7)^2 + (0 - 4)^2 = blank this results in a blank statement, so q(12, -3) blank on the circle. options: is, false, true, (5 - 12)^2 + (0 + 3)^2, is not, (12 - 7)^2 + (-3 - 4)^2

Explanation:

Step1: Calculate the radius squared

The radius squared \(r^{2}\) of the circle can be found using the distance formula between the center \((5,0)\) and the point \(M(7,4)\). The distance formula is \(d=\sqrt{(x_2 - x_1)^{2}+(y_2 - y_1)^{2}}\), and \(r^{2}=(x_2 - x_1)^{2}+(y_2 - y_1)^{2}\). For points \((5,0)\) and \((7,4)\), we have \((5 - 7)^{2}+(0 - 4)^{2}=(- 2)^{2}+(-4)^{2}=4 + 16=20\).

Step2: Check the distance from the center to \(Q(12,-3)\)

The distance squared from the center \((5,0)\) to the point \(Q(12,-3)\) is \((5 - 12)^{2}+(0+3)^{2}=(-7)^{2}+3^{2}=49 + 9=58\). Since \(58
eq20\) (the radius squared of the circle), the statement \((5 - 7)^{2}+(0 - 4)^{2}=(5 - 12)^{2}+(0 + 3)^{2}\) is false.

Answer:

First box: \((5 - 12)^{2}+(0 + 3)^{2}\)
Second box: false
Third box: is not