Question

# A diameter of a circle extends from (2,-7) to (5,-3)

Circles
A diameter of a circle extends from (2,-7) to (5,-3) what is the length of the circles radius?

2021-08-08
Step 1
Radius $$\displaystyle{y}={\frac{{{1}}}{{{2}}}}{x}$$ distance between points on diameter.
Points on diameter are (2,-7) and (5,-3)
So distance between $$\displaystyle{\left({x}_{{{1}}},{y}_{{{1}}}\right)}$$ and $$\displaystyle{\left({x}_{{{2}}},{y}_{{{2}}}\right)}$$ is
$$\displaystyle=\sqrt{{{\left({x}_{{{2}}}-{x}_{{{1}}}\right)}^{{{2}}}+{\left({y}_{{{2}}}-{y}_{{{1}}}\right)}^{{{2}}}}}$$
Step 2
So distance between (2,-7) and (5,-3) so
That $$\displaystyle=\sqrt{{{\left({5}-{2}\right)}^{{{2}}}+{\left(-{3}+{7}\right)}^{{{2}}}}}$$
$$\displaystyle=\sqrt{{{9}+{16}}}$$
$$\displaystyle=\sqrt{{{25}}}$$
$$\displaystyle={5}$$
So radius of circle $$\displaystyle={\frac{{{1}}}{{{2}}}}{x}{5}={25}$$