Directions in my book say, "find the coordinates of the other ENDPOINT of a segment with the given endpoint and midpoint M."
example: R(2,6)
M(-1,1)
I really need help.
I am assuming that (2,6) are the x and y coordinates of point R.
If the coordinates of the midpoint are (-1,1), the other endpoint has a decrease in x of -3, and a decrease of y by 5. (The same as from R to M)
That makes the coordinates of the other endpoint (-4, -4)
One way it to subtract the x values 2-(-1) = 3. Since that is 1/2 the line segment, then -1 -3 = -4 for the x value of the end of the other segment. The value of the y segment is done similarly (6-1 = 5 and 1-5 = -4 so the coordinates of the other end point is (-4,-4). You can check these values by plugging the values into y = mx + b to see if all satisfy the equation.
Oh. But I don't quite understand the process.
To find the coordinates of the other endpoint of a segment given the endpoint and midpoint, you can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a segment are the average of the coordinates of its endpoints.
In this case, you are given one endpoint R(2,6) and the midpoint M(-1,1).
To find the coordinates of the other endpoint, you can use the following steps:
Step 1: Write down the coordinates of the given endpoint and the midpoint.
R(2,6)
M(-1,1)
Step 2: Use the midpoint formula to find the coordinates of the other endpoint.
The midpoint formula is:
(x1 + x2)/2, (y1 + y2)/2
Let the other endpoint be P(x, y). Using the formula, we have:
(2 + x)/2 = -1 -> 2 + x = -2 -> x = -4
(6 + y)/2 = 1 -> 6 + y = 2 -> y = -4
Step 3: Write down the coordinates of the other endpoint.
P(-4,-4)
Therefore, the coordinates of the other endpoint of the segment are P(-4,-4).