Can someone help me with this algebra question?

Question

A line segment on the coordinate plane has endpoints (2,4) and (4,y). The midpoint of the segment is point (3,7). What is the value of y?

Answer 1

The midpoint (xm, ym) = (3, 7) of a line segment between (x1, y1) = (2, 4) and (x2, y2) = (4, y) is just the average of the endpoints.

(x1 + x2)/2 = xm
(2 + 4)/2 = 6/2 = 3, as expected.

(y1 + y2)/2 = ym
(4 + y)/2 = 7, so 4 + y = 14, so y = 10.

Answer 2

I'll try to show you with this picture.
If this is the line with the 3 points on it.
.___________.__________.
(2,4)_______(3,7)_______(4,y)

The midpoint (3,7) is the average of the two other points, so we could say that (3,7) = ([2+4]/2 , [4+y]/2).

This means that 3 = [2+4]/2
3 = 6 / 2
3 = 3

So the x coordinate of the midpoint is 3, which we already knew.

Now for the y coordinate.

Remember how (3,7) = ([2+4]/2 , [4+y]/2) meant that 3 = [2+4]/2.

This same method can be used for the 7.
7 = [4+y]/2
7 = 4/2 + y/2
7 = 2 + y/2
5 = y/2
10 = y

So, your midpoint would be (3,10).

It seems confusing, but you will get the hang of it with practice.
I hope I was helpful. Good luck!

Answer 3

Keep in mind that the midpoint of two points is determined by the following formula:

m = ( (x1 + x2)/2 , (y1 + y1)/2 )

Since we're actually given the midpoint to be (3,7), all we have to do is equate the coordinates of the midpoint component-wise. That is

(x1 + x2)/2 = 3
(y1 + y2)/2 = 7

Now, we know that (x1, y1) = (2, 4) and (x2, y2) = (4, y), and since we want to solve y, we only have to use the second equation.

(y1 + y2)/2 = 7
(4 + y)/2 = 7

And then we solve for y as normal. Multiplying both sides by 2,

4 + y = 14

y = 10

Answer 4

To find the midpoint of a line segment, find the average
of both coordiantes of the endpoints.
So the average of 2 and 4 is 3
and the average of 4 and y is 7.
So (4+y)/2 = 7
4 + y = 14
y = 10.
Hope that helps!

Answer 5

y = 10. The fastest way is to plot the three points on a piece of paper.

The formula for the line is y=3x-2. Substitute 4 for x and you get 10. This is the more formal way of doing it.

If you wonder how to get the slope of the line (3) or the intersection with the y-axis (-2), you find two points and divide the difference in the y's with the difference in the x's. The intersection, you get by using one of the points (and the slope)

Answer 6

for every one that x increases, y seems to increase by 3. So if x is four, then add 3 to 7, making it 10.

(4, 10)

As for the formula...

create a function where y is found by doing something to x:

f(x) = 3x - 2

I found this by finding a path to y that fit in both the starting point and the mid point. See below for finding the function.

You may now plug any number into x to find y.

Answer 7

Y equals 10

Answer 8

negative 3 ~~~