Math  /  Geometry

Question2. Find the coordinates of the midpoint of the segment with the given endpoints: A(0,0)A(0,0) and B(8,6)B(-8,6) A. (1,2)(1,2) B. (4,3)(-4,3) C. (2,1)(2,1) D. (3,4)(3,-4)

Studdy Solution

STEP 1

1. The formula for the midpoint M M of a line segment with endpoints A(x1,y1) A(x_1, y_1) and B(x2,y2) B(x_2, y_2) is given by: $ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
2. The given endpoints are \( A(0,0) \) and \( B(-8,6) \).

STEP 2

1. Identify the coordinates of the endpoints.
2. Apply the midpoint formula.
3. Calculate the midpoint coordinates.
4. Compare with the given options.

STEP 3

Identify the coordinates of the endpoints A A and B B .
- Endpoint A A has coordinates (0,0) (0,0) . - Endpoint B B has coordinates (8,6) (-8,6) .

STEP 4

Apply the midpoint formula:
Given the formula: M=(x1+x22,y1+y22)M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
Substitute the coordinates of A A and B B : M=(0+(8)2,0+62)M = \left( \frac{0 + (-8)}{2}, \frac{0 + 6}{2} \right)

STEP 5

Calculate the midpoint coordinates:
M=(82,62)M = \left( \frac{-8}{2}, \frac{6}{2} \right) M=(4,3)M = (-4, 3)

STEP 6

Compare the calculated midpoint with the given options:
The calculated midpoint is (4,3) (-4, 3) .
- Option A: (1,2) (1,2) - Option B: (4,3) (-4,3) - Option C: (2,1) (2,1) - Option D: (3,4) (3,-4)
The correct answer is Option B: (4,3) (-4,3) .
The coordinates of the midpoint of the segment are:
(4,3) \boxed{(-4,3)}

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