QuestionFind the midpoint of GH given G(7,-5) and H(9,-1).

Studdy Solution

STEP 1

Assumptions1. The coordinates of point G are (7, -5) . The coordinates of point H are (9, -1)
3. The midpoint of a line segment with endpoints (x1, y1) and (x, y) is given by the formula ((x1 + x)/, (y1 + y)/)

STEP 2

First, we need to find the x-coordinate of the midpoint. We can do this by adding the x-coordinates of G and H and then dividing by2.
$Midpoint_x = (x_G + x_H) /2$

STEP 3

Now, plug in the given values for the x-coordinates of G and H to calculate the x-coordinate of the midpoint.
$Midpoint_x = (7 +9) /2$

STEP 4

Calculate the x-coordinate of the midpoint.
$Midpoint_x = (7 +9) /2 =8$

STEP 5

Next, we need to find the y-coordinate of the midpoint. We can do this by adding the y-coordinates of G and H and then dividing by2.
$Midpoint_y = (y_G + y_H) /2$

STEP 6

Now, plug in the given values for the y-coordinates of G and H to calculate the y-coordinate of the midpoint.
$Midpoint_y = (-5 + -1) /2$

STEP 7

Calculate the y-coordinate of the midpoint.
$Midpoint_y = (-5 + -1) /2 = -3$

STEP 8

Now that we have both the x-coordinate and the y-coordinate of the midpoint, we can write the coordinates of the midpoint as a pair.
$Midpoint = (Midpoint_x, Midpoint_y)$

STEP 9

Plug in the values for the x-coordinate and the y-coordinate of the midpoint to write the coordinates of the midpoint.
$Midpoint = (8, -3)$ The midpoint of GH is (8, -3).

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