Does the point (-10,3) lie on the circle that passes through the point(-2,9) with center (-3,2)?

Circle is a set of points that have the same distance to the center (radius). You can calculate the radius in both cases. Distance between the center (-3,2) and the given point (-2,9) is sqrt((-3+2)^2+(2-9)^2) = sqrt(50) = 5sqrt(2). When you check the point in question (-10, 3), the distance is sqrt((-10+3)^2+(3-2(^2) = sqrt(50) = 5sqrt(2). Distance is the same so this point is on the circle (all the points with this distance from the center will be on the circle)

tutorconsortium005 tutorconsortium005 · Answer 2 · 2022-06-12T08:03:34+02:00

The point (-10,3) does not lie on the circle that passes through the point(-2,9) with the center (-3,2). So, option 4 is correct.

How to find the distance between two points?

The distance between two points (x1, y1) and (x2, y2) is calculated as

Distance = [tex]\sqrt{((x2-x1)^2+(y2-y1)^2}[/tex]

Calculation:

The given point is (-10,3)

Given that the circle passes through the point (-2,9) and the center at (-3,2)

So, the distance between the point and the center gives the radius of the circle.

Then,

The distance between the point (-2,9) and the center (-3,2) is

[tex]\sqrt{(-3+2)^2+(2-9)^2}[/tex]

⇒ [tex]\sqrt{(-1)^2+(-7)^2}[/tex]

⇒ [tex]\sqrt{1+49}[/tex]

⇒ [tex]\sqrt{50}=5\sqrt{2}[/tex]

So, the radius of the circle is [tex]5\sqrt{2}[/tex]

Since we know that all points that lie on the circle have the same distance from the center.

Then, for the point (-10,3), the distance from the center (-3,2) is

[tex]\sqrt{(-10-(-3))^2+(3-2)^2}\neq 5\sqrt{2}[/tex]

Therefore, they are not equal and the point (-10,3) does not lie on the given circle.

So, option 4 is correct.

Learn more about the distance between two points here:

https://brainly.com/question/23848540

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