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san4es73 [151]
2 years ago
14

One end of a line segment has the coordinates (-6,2). If

Mathematics
1 answer:
CaHeK987 [17]2 years ago
3 0

Answer:

The coordinates of the other end is (16,2)

Step-by-step explanation:

Given

End 1: (-6,2)

Midpoint: (5,2)

Required

Find the coordinates of the other end

Let Midpoint be represented by (x,y);

(x,y) = (5,2) is calculated as thus

(x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})

So

x = \frac{x_1 + x_2}{2} and y = \frac{y_1 + y_2}{2}

Where (x_1,y_1) = (-6,2) and (x,y) = (5,2)

So, we're solving for (x_2,y_2)

Solving for x_2

x = \frac{x_1 + x_2}{2}

Substitute 5 for x and -6 for x₁

5 = \frac{-6 + x_2}{2}

Multiply both sides by 2

2 * 5 = \frac{-6 + x_2}{2} * 2

10 = -6 + x_2

Add 6 to both sides

6 + 10 = -6 +6 +  x_2

x_2 = 16

Solving for y_2

y = \frac{y_1 + y_2}{2}

Substitute 2 for y and 2 for y₁

2 = \frac{2 + y_2}{2}

Multiply both sides by 2

2 * 2 = \frac{2 + y_2}{2} * 2

4 = 2 + y_2

Subtract 2 from both sides

4 - 2 = 2 - 2 + y_2

y_2 = 2

(x_2,y_2) = (16,2)

Hence, the coordinates of the other end is (16,2)

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