Question

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a circle is centered at q(1, -5) and has a radius of 5.
where does the point y(4, -1) lie?
choose 1 answer:
a inside the circle
b on the circle
c outside the circle

Explanation:

Step1: Calculate distance between center and point

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $(x_1,y_1)=(1,-5)$ (center $Q$) and $(x_2,y_2)=(4,-1)$ (point $Y$).
$d=\sqrt{(4 - 1)^2+(-1-(-5))^2}$

Step2: Simplify the expression

$d=\sqrt{3^2 + 4^2}=\sqrt{9 + 16}=\sqrt{25}=5$

Step3: Compare distance with radius

Radius $r = 5$, and $d = 5$. Since $d=r$, the point lies on the circle.

Answer:

B. On the circle