16. Points A, B, and C are collinear and A is between B and...

16. Points A, B, and C are collinear and A is between B and C. AB = 4x - 3, BC = 7x + 5, and AC = 5x - 16. Find each value. a. BC b. AB c. AC 17. On a number line, G = 8 and H = -3. If H is the midpoint of \overline{GI}, find the coordinate of I. 18. J is the midpoint of \overline{KL}. Find KJ if KL = 38.

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Transcript

00:01 To begin, let's decide which of our points is point one and which is point two.

00:05 Let's designate a as point one and b as point two.

00:11 Now let's begin to plug into our distance formula.

00:15 Distance formula is seen here in blue.

00:18 So, x2 is the x value of our second point.

00:22 So we have negative 3 minus our x1 value, which is the x value of our first point, which is 4, squared, plus y2, which is 8, minus y1, which is 7, also squared, plus z2, which is negative 8, minus z1, which is 9, also squared.

00:57 Now you'll notice we will be taking the square root of all of this, but first let's figure out what we're taking the square root up.

01:04 Well, negative 3 minus 4 is negative 7.

01:08 So we have negative 7 squared.

01:15 8, 9 .8.

01:15 Minus 7 is 1, and we'll be squaring that as well.

01:20 And then we have negative 8 minus 9.

01:22 Negative 8 minus 9 is negative 17, and we're squaring that.

01:32 Negative 7 squared is 49, because a negative times a negative is a positive.

01:38 1 squared is 1, and negative 17 squared is 289.

01:47 Now remember, negative 17 times negative 17, you're going to get a positive, so that's why it's positive 289.

01:54 When you add all these up, you get 339.

01:58 That is not the answer, however, because we need to take the square root of this as the formula dictates...

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