Video: The Distance between Two Points in Two Dimensions

What is the kind of triangle that points 𝐴 (9, βˆ’4), 𝐡 (3, 5), and 𝐢 (6, 1) form with respect to its angles?

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Video Transcript

What is the kind of triangle that points 𝐴 nine, negative four, 𝐡 three, five, and 𝐢 six, one form with respect to its angles?

The first thing we wanna do is sketch a graph we can use to graph the three points. From there, we’ll plot the three points 𝐴, 𝐡, and 𝐢. Point 𝐴 is located at nine, negative four: nine along the π‘₯-axis; negative four along the 𝑦-axis. Point 𝐡 is located at three along the π‘₯-axis and five along the 𝑦-axis. Point 𝐢 is located at six along the π‘₯-axis and one along the 𝑦-axis.

At first glance, it hardly seems like these three points will make a triangle at all, but we’re going to do our best to connect them. How do we label a triangle that looks like this? It has two very small angles and one very large angle.

To label this triangle by its angles, we look at angle 𝐢. And because we can visually tell that this is larger than 90 degrees, we label this as an obtuse triangle.

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