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3 years ago

B is the midpoint of AC. If AB= X +5 and BC = 2X -11, find the measure of AB

Mathematics

2 answers:

Murljashka [212]3 years ago

5 0

First, you know that B is the mid point, meaning AB is equal to BC. Therefore, you can set up the equation: x+5=2x-11. Then, you solve for x. Once you are done solving, you should get 16. Hope this helps!

Dahasolnce [82]3 years ago

3 0

Hi! Actually, the answer is 21. Because x+5 and 2x-11 are equivalent, set them equal to one another in an equation. Solve for x

You can see my steps in the picture i attached for you!!

Then, once you have x, you need to plug it back in to the expression x+5 (AB) to get 21. I hope this helps you!! :))

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The x-intercept of -2 gives us an idea that point (-2,0) if found along the line. The y-intercept of -1, tells us that point (0,-1), this also tells us that b = -1.

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$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Given two points} \\ (-2,0)\rightarrow(x_1,y_1) \\ (0,-1)\rightarrow(x_2,y_2) \\ \\ \text{Substitute} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-0}{0-(-2)} \\ m=-\frac{1}{2} \end{gathered}$

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$\begin{gathered} \text{Slope intercept form is} \\ y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \\ \\ \text{Substitute the values from before and we get} \\ y=-\frac{1}{2}x-1 \end{gathered}$

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