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r3t40

The midpoint can be defined using formula,

[tex]M(x_m=\dfrac{x_1+x_2}{2},y_m=\dfrac{y_1+y_2}{2})[/tex]

So by knowing [tex]x_m, x_1[/tex] and [tex]y_m, y_1[/tex] we can calculate [tex]x_2, y_2[/tex]

First we must derive two equations,

[tex]x_m=\dfrac{x_1+x_2}{2}\Longrightarrow x_2=2x_m-x_1[/tex]

and

[tex]y_m=\dfrac{y_1+y_2}{2}\Longrightarrow y_2=2y_m-y_1[/tex]

Then just put in the data,

[tex]x_2=2\cdot(-2)-3=-7[/tex]

[tex]y_2=2\cdot(-3)-0=-6[/tex]

So the other endpoint has coordinates [tex](x,y)\Longrightarrow(-7, -6)[/tex] therefore the answer is D.

Hope this helps.

r3t40

To work out the mid point of two points you, add the x coordinates and divide by 2, and you take the y coordinates and divide by two:

So:

[tex]midpoint = \frac{sum.of.x-coords}{2},  \frac{sum.of.y-coords}{2}[/tex]

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So the x-coords of the midpoint is:

[tex]\frac{sum.of.x-coords}{2}[/tex]

and

y -coords of midpoint is:

[tex]\frac{sum.of.y-coords}{2}[/tex]

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However, in this question we are trying to work out one of the endpoints.

First let's say that the coordinates of the missing endpoint is:

(x , y)

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That means that the x-coords of the midpoint of (x, y) and the other endpoint (3, 0) is :

[tex]\frac{3 + x}{2}[/tex]

However, we already know the x-coord of the midpoint ( it's -2). So we can form an equation to workout x:

[tex]\frac{3 + x}{2} = -2[/tex]                (multiply both sides by 2)

[tex]3 + x = -4[/tex]                      (subtract 3 from both sides)

[tex]x = -7[/tex]

This is the x-coord of the other endpoint

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Let's do the same for the y coordinates:

We know y coords for the midpoint of (x, y) and (3, 0) is:

[tex]\frac{0 + y}{2}[/tex]

But we also know the ycoord is -3. So we can form an equation and solve for y:

[tex]\frac{0+y}{2} = -3[/tex]

[tex]\frac{0 + y}{2} = -3[/tex]   (multiply both sides by 2)

[tex]0 + y = -6[/tex]                (simplify)

[tex]y = -6[/tex]

This is the y-coord of the other endpoint

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Now we just put these coords together to get the coordinate of the other endpoint:

Endpoint is at:

(x, y)                           (substitute in values that we worked out)

=  (-7, -6)

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Answer:

D. (-7, -6)

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Note:

If there is anything you don't quite understand or was unclear

- please don't hesitate to ask below in the comments.

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