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MissTica
2 years ago
7

One endpoint of a line segment has coordinates represented by (x+4,1/2y). The midpoint of the line segment is (3,−2).

Mathematics
1 answer:
lesya692 [45]2 years ago
3 0

Answer:

(-x+2, -\frac{1}{2}y-4})

Step-by-step explanation:

We know that one of the endpoints of the line segment is (x+4, 1/2y)

The midpoint of the line segment is (3, -2).

And we want to find the other coordinates in terms of x and y.

To do so, we can use the midpoint formula:

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

Since we know that the midpoint is (3, -2), let's substitute that for M:

(3, -2)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

Let's solve for each coordinate individually:

X-Coordinate:

We have:

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

We know that one of the endpoints is (x+4, 1/2y). So, let's let (x+4, 1/2y) be our (x₁, y₁). Substitute x+4 for x₁. This yields:

3=\frac{(x+4)+x_2}{2}

Solve for our second x-coordinate x₂. Multiply both sides by 2:

6=x+4+x_2

Subtract 4 from both sides:

2=x+x_2

Subtract x from both sides. Therefore, the x-coordinate of our second point is:

x_2=-x+2

Y-Coordinate:

We have:

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

Substitute 1/2y for y₁. This yields:

-2=\frac{\frac{1}{2}y+y_2}{2}

Solve for y₂. Multiply both sides by 2:

-4=\frac{1}{2}y+y_2

Subtract 1/2y from both sides. So:

y_2=-\frac{1}{2}y-4

Therefore, the other coordinate expressed in terms of x and y is:

(-x+2, -\frac{1}{2}y-4})

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Step-by-step explanation:

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Likewise, straightforward use of the calculator to find the other function values gives ...

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<em>Note on inverse tangent</em>

Depending on the mode setting of your calculator, the arctan or tan⁻¹ function may give you a value in degrees, not radians. That doesn't matter for this problem. sin(arctan(-0.087)) is the same whether the angle is degrees or radians, as long as you don't change the mode in the middle of the computation.

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<em>Alternate solution</em>

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This more complicated computation gives the same result as above.

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