Line Segment and Midpoint

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miisguiided_

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Hello! I'm having a tad bit of trouble with the following problem:

"Find the coordinates of the midpoint of the line segment joining (1,4) and (a, b), in terms of a and b. If (5, -1) is the midpoint, find the values of a and b."

I was able to work out the midpoint:
(1 + 4/2 , 4+b/2)

But I am unsure about how to go about finding the values of a and b.
If it helps the answer is that a = 9 and b = -6.

Any help would be much appreciated, thank you so much!!
 
The midpoint is \(\displaystyle (\frac{1+a}{2}, \frac{4+b}{2}) = (5, -1)\)
So \(\displaystyle \frac{1+a}{2} = 5 \) and \(\displaystyle \frac{4+b}{2}=-1\)
Solve those 2 equations and you'll have a and b.
 
miisguiided_ said:
Hello! I'm having a tad bit of trouble with the following problem:

"Find the coordinates of the midpoint of the line segment joining (1,4) and (a, b), in terms of a and b. If (5, -1) is the midpoint, find the values of a and b."

I was able to work out the midpoint:
(1 + 4/2 , 4+b/2)

But I am unsure about how to go about finding the values of a and b.
If it helps the answer is that a = 9 and b = -6.

Any help would be much appreciated, thank you so much!!
Click to expand...
Please observe that Harry corrected what you wrote. What you wrote means `(1 + 4/2, 4+b/2)`, where you omitted essential parentheses and typed 4 instead of a. You should have typed it as "((1+a)/2, (4+b)/2)", which means `((1+a)/2, (4+b)/2)`.
 
miisguiided_ said:
Hello! I'm having a tad bit of trouble with the following problem:

"Find the coordinates of the midpoint of the line segment joining (1,4) and (a, b), in terms of a and b. If (5, -1) is the midpoint, find the values of a and b."

I was able to work out the midpoint:
(1 + 4/2 , 4+b/2)

But I am unsure about how to go about finding the values of a and b.
If it helps the answer is that a = 9 and b = -6.

Any help would be much appreciated, thank you so much!!
Click to expand...
x goes from 1 to 5, an increase of 4. The x value of the midpoint will have an increase from 1 of half of 4. So the x value of the midpoint will be ??
y goes from 4 to -1, a decrease of 5. The y value of the midpoint will have a decrease from 4 of half of 5. So the y value of the midpoint will be ??
 
Jomo said:
x goes from 1 to 5, an increase of 4. The x value of the midpoint will have an increase from 1 of half of 4. So the x value of the midpoint will be ??
y goes from 4 to -1, a decrease of 5. The y value of the midpoint will have a decrease from 4 of half of 5. So the y value of the midpoint will be ??
Click to expand...
No, you've misread the problem: (5, -1) is the midpoint, not one end. We are given the midpoint, not asked for it.

But what you say can be turned inside out to solve the problem without algebra. If x increases by 4 from one end to the midpoint, then it must increase by another 4 to the far endpoint. Where will that be?
 
Jomo said:
x goes from 1 to 5, an increase of 4. The x value of the midpoint will have an increase from 1 of half of 4. So the x value of the midpoint will be ??
y goes from 4 to -1, a decrease of 5. The y value of the midpoint will have a decrease from 4 of half of 5. So the y value of the midpoint will be ??
Click to expand...
Jomo opens 2021 with corner time......
 
Harry_the_cat said:
The midpoint is \(\displaystyle (\frac{1+a}{2}, \frac{4+b}{2}) = (5, -1)\)
So \(\displaystyle \frac{1+a}{2} = 5 \) and \(\displaystyle \frac{4+b}{2}=-1\)
Solve those 2 equations and you'll have a and b.
Click to expand...
thank you! this makes so much more sense now!
 
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