Question

P is the midpoint of CX. Given P(-2,4) and C(-5,7), find the coordinates of X.

a) X(-8, 2)
b) X(-11, 1)
c) X(1, -8)
d) X(8, -2)

Answer 1

a) X(-8, 2) because The coordinates of point X are found using the midpoint formula, yielding X(-8, 2) and confirming option (a) as the correct answer.

Step-by-step explanation:

The midpoint formula is given by
`\( P(x, y) = \left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right) \)`, where
`\( P(x, y) \) is the midpoint, and \( (x_1, y_1) \) and \( (x_2, y_2) \)` are the coordinates of the two endpoints.

In this case,
`\( P(-2, 4) \) is the midpoint of \( C(-5, 7) \) and \( X(x, y) \)`. Using the midpoint formula, we can set up two equations:

`\[ -2 = \frac{{-5 + x}}{2} \]\[ 4 = \frac{{7 + y}}{2} \]`

Solving these equations gives
`\( x = -8 \) and \( y = 2 \)`, which corresponds to the coordinates of point X. Therefore, the correct answer is
`\( X(-8, 2) \)`, and the final answer is option (a).

This means that the point X is indeed (-8, 2), making option (a) the correct choice. The midpoint formula essentially finds the average of the x-coordinates and y-coordinates of two points, giving us the coordinates of the midpoint. This property allows us to determine the missing endpoint when the midpoint and one endpoint are known.