Question

A circle is centered at R(2,4). The point L(0,8) is on the circle. Where does the point Q(6,7) lie?

A. Inside the circle
B. On the circle
C. Outside the circle

Answer 1

To determine the position of point Q(6,7) relative to the circle centered at R(2,4) with point L(0,8) on the circumference, calculate the radius of the circle and the distance from Q to R. The calculated radius is √20 and the distance from Q to R is 5. Because the distance is less than the radius, point Q lies inside the circle.

The Correct Option is ; A. Inside the circle.

Step-by-step explanation:

The student's question pertains to the location of a point relative to a circle in a coordinate plane. Given the circle is centered at R(2,4), and a point on the circle is L(0,8), the radius of the circle can be determined. To find out whether the point Q(6,7) lies inside, on, or outside the circle, the distance from Q to the center R can be compared to the radius.

First, let's calculate the radius using the distance formula between the center R(2,4) and a known point on the circle L(0,8):

Radius = √((x2 - x1) ² + (y2 - y1) ²)
Radius = √((2 - 0) ² + (4 - 8) ²)
Radius = √(4 + (-4) ²)
Radius = √(4 + 16)
Radius = √20

Now, we find the distance from Q(6,7) to the center R:

Distance = √((x2 - x1) ² + (y2 - y1) ²)
Distance = √((6 - 2) ² + (7 - 4) ²)
Distance = √(16 + 9)
Distance = √25 = 5

Since the distance from Q to R is 5, which is less than the radius (√20 ≈ 4.47), point Q(6,7) lies inside the circle.