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3 years ago

Find the value of x if A,B,and C are collinear points and B is between A and C. AB=3x, BC=2x-7, AC=2x+35

Mathematics

2 answers:

Mariana [72]3 years ago

6 0

Answer:

x = 14

Step-by-step explanation:

3x+2x-7=2x+35

then solve for x

bekas [8.4K]3 years ago

3 0

Answer:

x = 14

Step-by-step explanation:

We are given that A, B and C are collinear points and B is in between A and C.

The length from A to B is $3 x$ , length from B to C is $2x - 7$ and AC is $2 x + 35$ .

We are to find the value of x.

$A B + B C = A C$

$3 x + 2 x - 7 = 2 x + 3 5$

$3 x + 2 x - 2 x = 3 5 + 7$

$3 x = 4 2$

$x = \frac { 4 2 } { 3 }$

x = 14

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Line Equation from Two Points

Verdich [7]

Hi!

We can use point-slope form to solve this.

$y-y_{1} =m(x -x_{1})$

$y_{1}$ and $x_{1}$ will be from one of the points.

First, we have to find $m$ , the slope. We can use the slope equation to get this.

$\frac{y_{1} -y_{2} }{x_{1} -x_{2} }$

Plug in your points:

$\frac{4-0}{8-(-8)} =\frac{4-0}{8+8} =\frac{4}{16} =\frac{1}{4}$

Your slope is $\frac{1}{4}$

Now plug points and slope into point-slope equation. We will use (8, 4).

$y-4=\frac{1}{4} (x-8)$

Now, if you want to get it into y = mx + b form, you have to solve for y:

$y-4=\frac{1}{4} (x-8)$

$y-4=\frac{1}{4} x-2$

$y=\frac{1}{4} +2$

Your equation is $y=\frac{1}{4} +2$

For more information on how to get the equation of a line when given two points, see here:

brainly.com/question/986503

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1 year ago