Question

Circle O has a center at (-2, 10) and a

Answer 1

Answer:

B

Step-by-step explanation:

If the point lies on the circle, the distance of the point to the center would be equivalent to the circle's radius since radius is defined as the distance from the center to any point of the circle.

Since length of a radius is half of a diameter,

radius= diameter ÷2

radius= 12 ÷2

radius= 6 units

Let's find the length between each points to see which is equal to 6 units, using the distance formula below.

$distance = \sqrt{(y1 - y2)^{2} + {(x1 - x2)}^{2} }$

A. Distance between 2 points

$= \sqrt{ {(10 + 5)}^{2} + ( - 2 + 6)^{2} } \\ = \sqrt{15 ^{2} + {4}^{2}} \\ = \sqrt{241} \\ = 15.524 \: units$

(to 5 s.f.)

Since the distance is greater than 6 units, point A lies outside the circle.

B. Distance between 2 points

$= \sqrt{ {(10 - 4)}^{2} + ( - 2 + 2)^{2} } \\ = \sqrt{ {6}^{2} } \\ = 6 \: units$

Since the distance of B from the center is 6 units, point B lies on Circle O.

Let's check the other 2 points:

C. Distance between 2 points

$= \sqrt{ {(10 - 4)}^{2} + {( - 2 - 6)}^{2} } \\ = \sqrt{ {6}^{2} + ( - 8)^{2} } \\ = \sqrt{100} \\ = 10 \: units$

Since the distance of point C from the center is greater than 6 units, point C lies outside the circle.

D. Distance between 2 points

$= \sqrt{ {(10 - 8)}^{2} + {( - 2 - 8)}^{2} } \\ = \sqrt{2^{2} + ( - 10)^{2} } \\ = \sqrt{104} \\ = 10.198 \: units$

(to 5 s.f.)

Point D also lies outside Circle O.