Final answer:
In this case, the points that also lie on the circumference of the circle are: (-12, -5), (-10, 12) and(-5, -12).
The answer is option ⇒A,D and E
Step-by-step explanation:
To determine which points lie on the circumference of a circle centered at the origin, we need to find the radius of the circle. The radius is the distance from the center of the circle to any point on its circumference.
Given that the center of the circle is at the origin (0, 0) and a point (-5, 12) lies on the circumference, we can calculate the distance between the origin and (-5, 12) using the distance formula.
Distance = √((x₂ - x₁)²+ (y₂ - y₁)²)
Distance = √((0 - (-5))² + (0 - 12)²)
Distance = √(5² + 12²)
Distance = √(25 + 144)
Distance = √169
Distance = 13
So, the radius of the circle is 13 units.
Now, let's check which points lie on the circumference of the circle by calculating the distance between the origin and each of the given points:
a. (-12, -5)
- Distance = √((0 - (-12))² + (0 - (-5))²)
- Distance = √(12² + 5²)
- Distance = √(144 + 25)
- Distance = √169
- Distance = 13
b. (-12, -1)
- Distance = √((0 - (-12))² + (0 - (-1))²)
- Distance = √(12² + 1²)
- Distance = √(144 + 1)
- Distance = √145
c. (-10, -12)
- Distance = √((0 - (-10))² + (0 - (-12))²)
- Distance = √(10² + 12²)
- Distance = √(100 + 144)
- Distance = √244
d. (-10, 12)
- Distance = √((0 - (-10))² + (0 - 12)²)
- Distance = √(10² + 12²)
- Distance = √(100 + 144)
- Distance = √244
e. (-5, -12)
- Distance = √((0 - (-5))² + (0 - (-12))²)
- Distance = √(5² + 12²)
- Distance = √(25 + 144)
- Distance = √169
- Distance = 13
From the calculations, we can see that points a (-12, -5), e (-5, -12), and d (-10, 12) lie on the circumference of the circle.
Therefore, the points that also lie on the circumference of the circle are:
a. (-12, -5)
d. (-10, 12)
e. (-5, -12)
The answer is option ⇒A,D and E