Which of the following points lies on the circle whose center is at the origin and whose radius is 10
(-6,4)
(/10,/10)
(6,-8)
To determine which of the given points lies on the circle with center at the origin and radius of 10, we can use the distance formula.
The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance between each given point and the origin (0, 0):
1. For the point (-6, 4):
d = √((-6 - 0)^2 + (4 - 0)^2)
= √(36 + 16)
= √52
≈ 7.211
2. For the point (/10, /10):
d = √((/10 - 0)^2 + (/10 - 0)^2)
= √((10/√2)^2 + (10/√2)^2)
= √(100/2 + 100/2)
= √(100)
= 10
3. For the point (6, -8):
d = √((6 - 0)^2 + (-8 - 0)^2)
= √(36 + 64)
= √100
= 10
From the calculated distances, we can see that the point (/10, /10) lies on the circle with center at the origin and radius of 10.
To determine if a point lies on a circle, we need to calculate the distance between the point and the center of the circle and compare it to the radius of the circle.
Let's calculate the distance between each point and the origin (center of the circle) using the distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
For point (-6, 4):
Distance = √((0 - (-6))² + (0 - 4)²)
= √((6)² + (-4)²)
= √(36 + 16)
= √52
≈ 7.211
For point (/10, /10):
Distance = √((0 - (/10))² + (0 - (/10))²)
= √((/10)² + (/10)²)
= √((/100) + (/100))
= √(/200)
≈ 4.472
For point (6, -8):
Distance = √((0 - 6)² + (0 - (-8))²)
= √((-6)² + (8)²)
= √(36 + 64)
= √100
= 10
Comparing the calculated distances with the radius, we can see that:
- For point (-6, 4), the distance is approximately 7.211, which is less than the radius of 10. Hence, this point lies inside the circle.
- For point (/10, /10), the distance is approximately 4.472, which is less than the radius of 10. Hence, this point also lies inside the circle.
- For point (6, -8), the distance is 10, which is equal to the radius of 10. Hence, this point lies on the circle.
Therefore, the point (6, -8) is the only point that lies on the circle whose center is at the origin and radius is 10.
you need x^2+y^2 = 100
So, which point works?