Point $$A$$ is at $$(-4,8)$$ and point $$M$$ is at $$(1,7.5)$$.

Point $$M$$ is the midpoint of point $$A$$ and point $$B$$.

What are the coordinates of point $$B$$ ? 

![](http://admin.getprephub.com/media/editor/ag6_20230214202140004266.png)

<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>Point $$A$$ is at $$(-4,8)$$ and point $$M$$ is at $$(1,7.5)$$.

Point $$M$$ is the midpoint of point $$A$$ and point $$B$$.

What are the coordinates of point $$B$$ ? 

![](http://admin.getprephub.com/media/editor/ag6_20230214202140004266.png)</textarea>Point <math><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math>A is at <math><semantics><mrow><mo>(</mo><mo>−</mo><mn>4</mn><mo separator="true">,</mo><mn>8</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(-4,8)</annotation></semantics></math>(−4,8) and point <math><semantics><mrow><mi>M</mi></mrow><annotation encoding="application/x-tex">M</annotation></semantics></math>M is at <math><semantics><mrow><mo>(</mo><mn>1</mn><mo separator="true">,</mo><mn>7</mn><mi mathvariant="normal">.</mi><mn>5</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(1,7.5)</annotation></semantics></math>(1,7.5).
Point <math><semantics><mrow><mi>M</mi></mrow><annotation encoding="application/x-tex">M</annotation></semantics></math>M is the midpoint of point <math><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math>A and point <math><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math>B.
What are the coordinates of point <math><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math>B ? 
<img src="http://admin.getprephub.com/media/editor/ag6_20230214202140004266.png" alt="">
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>Let, $$M(1,7.5)$$ is the midpoint of $$A(-4,8)$$ and $$B(x, y)$$ 
By midpoint formula, $$(\frac{-4+x}{2}, \frac{y+8}{2})=(1,7.5)$$
By Comparing.
$$ \frac{x-4}{2}=1 $$
$$ \text { or, } x=6 $$
$$ \frac{y+8}{2}=7.5 $$
$$ y+8=15$$
$$ y=7$$
$$(6,7)$$ is the co-ordinate of $$B$$.
</textarea>Let, <math><semantics><mrow><mi>M</mi><mo>(</mo><mn>1</mn><mo separator="true">,</mo><mn>7</mn><mi mathvariant="normal">.</mi><mn>5</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">M(1,7.5)</annotation></semantics></math>M(1,7.5) is the midpoint of <math><semantics><mrow><mi>A</mi><mo>(</mo><mo>−</mo><mn>4</mn><mo separator="true">,</mo><mn>8</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">A(-4,8)</annotation></semantics></math>A(−4,8) and <math><semantics><mrow><mi>B</mi><mo>(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">B(x, y)</annotation></semantics></math>B(x,y) By midpoint formula, <math><semantics><mrow><mo>(</mo><mfrac><mrow><mo>−</mo><mn>4</mn><mo>+</mo><mi>x</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo separator="true">,</mo><mfrac><mrow><mi>y</mi><mo>+</mo><mn>8</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo><mo>=</mo><mo>(</mo><mn>1</mn><mo separator="true">,</mo><mn>7</mn><mi mathvariant="normal">.</mi><mn>5</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(\frac{-4+x}{2}, \frac{y+8}{2})=(1,7.5)</annotation></semantics></math>(​2​​−4+x​​,​2​​y+8​​)=(1,7.5) By Comparing. <math><semantics><mrow><mfrac><mrow><mi>x</mi><mo>−</mo><mn>4</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex"> \frac{x-4}{2}=1 </annotation></semantics></math>​2​​x−4​​=1 <math><semantics><mrow><mtext><mtext>&nbsp;</mtext><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">,</mi><mtext>&nbsp;</mtext></mtext><mi>x</mi><mo>=</mo><mn>6</mn></mrow><annotation encoding="application/x-tex"> \text { or, } x=6 </annotation></semantics></math>&nbsp;or,&nbsp;x=6 <math><semantics><mrow><mfrac><mrow><mi>y</mi><mo>+</mo><mn>8</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>=</mo><mn>7</mn><mi mathvariant="normal">.</mi><mn>5</mn></mrow><annotation encoding="application/x-tex"> \frac{y+8}{2}=7.5 </annotation></semantics></math>​2​​y+8​​=7.5 <math><semantics><mrow><mi>y</mi><mo>+</mo><mn>8</mn><mo>=</mo><mn>1</mn><mn>5</mn></mrow><annotation encoding="application/x-tex"> y+8=15</annotation></semantics></math>y+8=15 <math><semantics><mrow><mi>y</mi><mo>=</mo><mn>7</mn></mrow><annotation encoding="application/x-tex"> y=7</annotation></semantics></math>y=7 <math><semantics><mrow><mo>(</mo><mn>6</mn><mo separator="true">,</mo><mn>7</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(6,7)</annotation></semantics></math>(6,7) is the co-ordinate of <math><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math>B.
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