Math  /  Geometry

QuestionFind the midpoint of the line segment joining the points R(2,3)R(-2,3) and S(4,6)S(4,6).
The midpoint is \square (Type an ordered pair. Use integers or simplified fractions for any numbers in the expression.)

Studdy Solution

STEP 1

1. The points given are R(2,3) R(-2, 3) and S(4,6) S(4, 6) .
2. The midpoint formula for a line segment in a 2D plane is applicable.

STEP 2

1. Recall the formula for the midpoint of a line segment.
2. Substitute the coordinates of the given points into the formula.
3. Calculate the midpoint.

STEP 3

Recall the formula for the midpoint of a line segment joining two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):
M=(x1+x22,y1+y22) M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)

STEP 4

Substitute the coordinates of the points R(2,3) R(-2, 3) and S(4,6) S(4, 6) into the formula:
M=(2+42,3+62) M = \left( \frac{-2 + 4}{2}, \frac{3 + 6}{2} \right)

STEP 5

Calculate the midpoint:
M=(2+42,3+62) M = \left( \frac{-2 + 4}{2}, \frac{3 + 6}{2} \right) =(22,92) = \left( \frac{2}{2}, \frac{9}{2} \right) =(1,92) = (1, \frac{9}{2})
The midpoint of the line segment is:
(1,92) \boxed{\left( 1, \frac{9}{2} \right)}

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