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Video: Determining Which of a Group of Points Lies Inside the Shown Circle

Tim Burnham

Which of the points below is inside the circle? [A] (−2, −9) [B] (5, 1) [C] (7, −6) [D] (8, −5) [E] (7, −9)

02:24

Video Transcript

Which of the points is inside the circle? Now we’ve been given a Cartesian plane with a circle on it, and we’ve been given five points with their coordinates: negative two, negative nine; five, one; seven, negative six; eight, negative five; and seven, negative nine. So let’s go through them one by one, plot them on the coordinate plane, and see which ones are inside the circle.

Now remember with coordinates, the first number is the 𝑥-coordinate and the second number is the 𝑦-coordinate, and remember 𝑥 comes before 𝑦 in the alphabet, so the 𝑥 number comes before the 𝑦 number in our coordinate pair.

So the 𝑥 number tells you how far to move in the 𝑥-direction and the 𝑦 number tells you how far to move in the 𝑦-direction. And we always start off at zero, zero when working out where the coordinates are.

So for point A, we start off at zero, zero and we go negative two in the 𝑥-direction and negative nine in the 𝑦-direction, which means we end up here. Well that’s not inside the circle.

Let’s look at point B. That’s starting at zero, zero, positive five in the 𝑥-direction and positive one in the 𝑦-direction; we end up here. That’s not inside the circle.

Now point C, starting off at zero, zero, we move positive seven in the 𝑥-direction and negative six in the 𝑦-direction, which means we end up here. Now that is inside the circle.

Now point D, we start off at zero, zero, and we go positive eight in the 𝑥-direction and negative five in the 𝑦-direction, which just leaves us here. And that’s just outside the circle, so that’s not inside the circle.

And lastly point E, starting off at zero, zero, we go positive seven in the 𝑥-direction and negative nine in the 𝑦-direction, bringing us down to here. And that is also outside the circle, so it’s not inside the circle. So the answer is C. The point seven, negative six is inside the circle.