Find the midpoint of A(5, 8) and B(-1, -4)

Understand the Problem

The question is asking to find the midpoint between the two given points A(5, 8) and B(-1, -4) using the midpoint formula. The midpoint formula is given by ((x1 + x2)/2, (y1 + y2)/2).

Answer

The midpoint is $ M(2,2) $.

Steps to Solve

Identify coordinates of points A and B
The coordinates for point A are ( A(5, 8) ) and for point B are ( B(-1, -4) ).
Apply the midpoint formula
The midpoint formula is given by

$$ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) $$

Substituting ( A(5, 8) ) and ( B(-1, -4) ) into the formula, we have:

( x_1 = 5 ), ( y_1 = 8 )
( x_2 = -1 ), ( y_2 = -4 )

Calculate the x-coordinate of the midpoint
Now, calculate the x-coordinate:

$$ x_m = \frac{5 + (-1)}{2} = \frac{4}{2} = 2 $$

Calculate the y-coordinate of the midpoint
Next, calculate the y-coordinate:

$$ y_m = \frac{8 + (-4)}{2} = \frac{4}{2} = 2 $$

Combine the results
The midpoint ( M ) is therefore:

$$ M = (x_m, y_m) = (2, 2) $$

The midpoint is ( M(2, 2) ).

More Information

The midpoint is the average of the x-coordinates and the average of the y-coordinates of the two points. It represents the point that is exactly halfway between the two points.

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