Question

Please help Geometry High School

Answer 1

`\sqrt20`

Explanation:

Just by looking at the graph, we can see that the x value of the center of the circle has to be positive and the y value negative. Only the first and last choices fit this. and (5, -3) is at the center. (3,-1) is nowhere near the center. So your choice is correct

The radius of the circle will be the distance from the center to any point on the circle

We know the center is at (5, -3) and the circle passes through (3,1). So we have to find the distance between these two points. Call it r

By the Pythagorean theorem, distance, r between any two points on a 2-D coordinate is given by

`r = \sqrt{(x2-x1)^2 + (y2-y1)^2`

where the coordinates of the two points are (x1, y1) and (x2, y2)

We have x2 = 3, x1=5 and y2 = 1, y1 = -3

r =
`\sqrt\\(3-5)^2 + (-1-3)^2\\` =
`\sqrt\\(-2)^2 + (-4)^2` =
`\sqrt\\4+16` =
`\sqrt20`