Point $$A$$ is at $$(3,-8)$$ and point $$B$$ is at $$(7,3)$$. What is the midpoint of line segment $$A \boldsymbol{B}$$ ? 

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<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>Point $$A$$ is at $$(3,-8)$$ and point $$B$$ is at $$(7,3)$$. What is the midpoint of line segment $$A \boldsymbol{B}$$ ? 

![](https://cdn.mathpix.com/cropped/2023_02_06_a5ce451859c01906b20fg-04.jpg?height=1330width=1339top_left_y=283top_left_x=290)

</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><mn>3</mn><mo separator="true">,</mo><mo>−</mo><mn>8</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(3,-8)</annotation></semantics></math>(3,−8) and point <math><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math>B is at <math><semantics><mrow><mo>(</mo><mn>7</mn><mo separator="true">,</mo><mn>3</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(7,3)</annotation></semantics></math>(7,3). What is the midpoint of line segment ? 
<img src="https://cdn.mathpix.com/cropped/2023_02_06_a5ce451859c01906b20fg-04.jpg?height=1330width=1339top_left_y=283top_left_x=290" alt="">
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>Let $$A(3,-8)$$ and $$B(7,3)$$ are the co-ordinates of $$A$$ and $$B$$.

let, $$M(x, y)$$ is the midpoint of $$A B$$. By midpoint formula, $$(\frac{3+7}{2},\frac{-8+3}{2})=(x, y)$$

or $$(5,-\frac{5}{2})=(x, y)$$

The co-ordinate of $$M$$ is $$(5,-\frac{5 }{2})$$ </textarea>Let <math><semantics><mrow><mi>A</mi><mo>(</mo><mn>3</mn><mo separator="true">,</mo><mo>−</mo><mn>8</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">A(3,-8)</annotation></semantics></math>A(3,−8) and <math><semantics><mrow><mi>B</mi><mo>(</mo><mn>7</mn><mo separator="true">,</mo><mn>3</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">B(7,3)</annotation></semantics></math>B(7,3) are the co-ordinates of <math><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math>A and <math><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math>B.
let, <math><semantics><mrow><mi>M</mi><mo>(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">M(x, y)</annotation></semantics></math>M(x,y) is the midpoint of <math><semantics><mrow><mi>A</mi><mi>B</mi></mrow><annotation encoding="application/x-tex">A B</annotation></semantics></math>AB. By midpoint formula, <math><semantics><mrow><mo>(</mo><mfrac><mrow><mn>3</mn><mo>+</mo><mn>7</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo separator="true">,</mo><mfrac><mrow><mo>−</mo><mn>8</mn><mo>+</mo><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">(\frac{3+7}{2},\frac{-8+3}{2})=(x, y)</annotation></semantics></math>(​2​​3+7​​,​2​​−8+3​​)=(x,y)
or <math><semantics><mrow><mo>(</mo><mn>5</mn><mo separator="true">,</mo><mo>−</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">(5,-\frac{5}{2})=(x, y)</annotation></semantics></math>(5,−​2​​5​​)=(x,y)
The co-ordinate of <math><semantics><mrow><mi>M</mi></mrow><annotation encoding="application/x-tex">M</annotation></semantics></math>M is <math><semantics><mrow><mo>(</mo><mn>5</mn><mo separator="true">,</mo><mo>−</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><annotation encoding="application/x-tex">(5,-\frac{5 }{2})</annotation></semantics></math>(5,−​2​​5​​) 
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