Question

What are the coordinates of point X if the midpoint is M(-3, -1) and Y is (8, -6)?

A) X(-14, 1)
B) X(1, 2.5)
C) X(3, 1)
D) X(-5.5, -3.5)

Answer 1

Using the midpoint formula, we solve for the coordinates of point X with M(-3, -1) and Y(8, -6), finding them to be (-14, 4), which is not listed in the provided options.

Step-by-step explanation:

To find the coordinates of point X when given the midpoint M and one endpoint Y, we can use the midpoint formula, which is a standard topic in high school mathematics.

The midpoint M of a line segment with endpoints X(x1, y1) and Y(x2, y2) is calculated as M = ((x1+x2)/2, (y1+y2)/2). We're given M(-3, -1) and Y(8, -6), so we set up the following equations to solve for the coordinates of X:

Mx = (Xx + Yx)/2 and My = (Xy + Yy)/2

By substituting the values for M and Y, we get:

-3 = (Xx + 8)/2
-1 = (Xy - 6)/2

Solving these equations gives us Xx = -14 and Xy = 4. Therefore, the correct coordinates for point X are (-14, 4), which suggests there may be an error in the options provided.