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QuestionFind the midpoint of GH‾\overline{\mathrm{GH}} with endpoints G(14,3)G(14,3) and H(10,−6)H(10,-6). Choices: A. (6,−15)(6,-15) B. (−2,−92)\left(-2,-\frac{9}{2}\right) C. (12,−32)\left(12,-\frac{3}{2}\right) D. (24,−3)(24,-3) E. (18,12)(18,12).

Studdy Solution

STEP 1

Assumptions1. The coordinates of point G are (14,3) . The coordinates of point H are (10,-6)
3. We are looking for the midpoint of the line segment GH

STEP 2

The formula for the midpoint of a line segment with endpoints (x1,y1)(x1, y1) and (x2,y2)(x2, y2) is given by(x1+x22,y1+y22)(\frac{x1+x2}{2},\frac{y1+y2}{2})

STEP 3

Now, plug in the given values for the coordinates of points G and H into the midpoint formula.
(14+102,3+(−6)2)(\frac{14+10}{2},\frac{3+(-6)}{2})

STEP 4

Calculate the x-coordinate of the midpoint.
14+102=12\frac{14+10}{2} =12

STEP 5

Calculate the y-coordinate of the midpoint.
3+(−)2=−32\frac{3+(-)}{2} = -\frac{3}{2}

STEP 6

The midpoint of the line segment GH is therefore(12,−32)(12,-\frac{3}{2})So, the correct answer is C. (12,−32)\left(12,-\frac{3}{2}\right).

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