Mathematics, 16.02.2020 07:14, xDANTEx2456

Please help !! My friend has a math test tomorrow and he is struggling to answer this:

Find the equation of a straight line that has a perpendicular bisector of AB.
A = (2,6) B = (5, -2)

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answered: sabahtramirez01

So the line that is a perpendicular bisector of AB is $y=\frac{3}{8}x+\frac{11}{16}$ .

Step-by-step explanation:

If we are looking for a line such that is is perpendicular bisector of AB, then we first need to find the midpoint of AB.

The midpoint of AB is going to be the "average" point.

What I mean by this, to find the x-coordinate of the midpoint we need to average our x-coordinates of our endpoints and we also need to do the same for the y-coordinate part.

Let's begin this.

The average of the x-coordinates of the endpoints are:

$\frac{2+5}{2}=\frac{7}{2}$

The average of the y-coordinates of the endpoints are:

$\frac{6+(-2)}{2}=\frac{4}{2}=2$

This concludes the midpoint of AB is $(\frac{7}{2},2)$ .

Now we also need to calculate the slope of so we can find the slope of the line perpendicular to it.

To do this we could use $\frac{y_2-y_1}{x_2-x_1}$ . Without using the formula directly, I like to line the points up vertically and subtract. I then put the 2nd difference over the first difference. Like so,

(5,-2)

- (2,6)

----------------------

3 , -8

So the slope is $\frac{-8}{3}$ .

The line that is perpendicular to the line AB will have an opposite reciprocal slope.

So the line we are looking for has slope $\frac{3}{8}$ .

So we are looking for a line going through the midpoint $(\frac{7}{2},2)$ and has slope $\frac{3}{8}$ .

A line in slope-intercept form is y=mx+b .

We know $m=\frac{3}{8}{/tex] and we know a point [tex](x,y)=(\frac{7}{2},2)$ . We could plug this in to find .

Let's do that now.

$2=\frac{3}{8}(\frac{7}{2})+b$

Simplify:

$2=\frac{21}{16}+b$

Subtract 21/16 on both sides:

$2-\frac{21}{16}=b$

Find a common denominator:

$\frac{32}{16}-\frac{21}{16}$

$\frac{11}{16}$

So the line that is a perpendicular bisector of AB is $y=\frac{3}{8}x+\frac{11}{16}$ . This is so because the line we found will be perpendicular to AB while also cutting AB into two equal halves.

answered: Guest

Answer: choice c and choice d

=====================================

explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

Which functions have an additive rate of change of 3? check all that apply

answered: Guest

step-by-step explanation:

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