Question

B is the midpoint of AC and E is the midpoint of BD. If A (-9,-4), C(-1,6), and E(-4,-3), find the coordinates of D.

Answer 1

The coordinates of D are (-3, -7)

First we need to find the coordinates of B. In order to do that we simply take the average of the two points that make up the segment for which it is the midpoint (A and C).

Average of x's

-9 + -1 = -10/2 = -5

Average of y's

-4 + 6 = 2/2 = 1

Therefore, the coordinates of B are (-5, 1).

Now we can find D by noting the E will be the average of B and D. So we can use the average equation to determine the values of D.

Average of x's

(B + D)/2 = E

(-5 + D)/2 = -4

-5 + D = -8

D = -3

Average of y's

(B + D)/2 = E

(1 + D)/2 = -3

1 + D = -6

D = -7

Now we know the coordinates of D to be (-3, -7)

Answer 2

The coordinates of D are D(-3,-7).

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This question is solved using the midpoint concept, the midpoint of a segment is the mean of it's coordinates.

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Point B:

B(x,y) is the midpoint of A(-9,-4) and C(-1,6), so:

$x = \frac{-9 - 1}{2} = -5$

$y = \frac{-4 + 6}{2} = 1$

Thus, the coordinates of B are B(-5,1).

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Point D:

E(-4,-3) is the midpoint of B(-5,1) and D(x,y), so:

The x-coordinate of D is:

$-4 = \frac{-5 + x}{2}$

$-5 + x = -8$

$x = -3$

The y-coordinate of D is:

$-3 = \frac{1 + y}{2}$

$1 + y = -6$

$y = -7$

The coordinates of D are D(-3,-7).

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