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Point A is located at (−1,−5). The midpoint of line segment AB is point C(2,3). ​ What are the coordinates of point B ?

Respuesta :

Danboghiu66

For a segment AB, the coordinates of the middle point C are:

xc=(xa+xb)/2,

yc=(ya+yb)/2.

Now, you know points A and C. Thus we get:

xb=2×xc-xa

yb=2×yc-ya

With numerical values:

xb=2×2-(-1)=4+1=5

yb=2×3-(-5)=6+5=11

Answer: B(5, 11)

MrRoyal

The midpoint of a line segment divides the line into equal parts.

The coordinates of B is (5,11)

The given parameters are:

[tex]\mathbf{A = (-1.-5)}[/tex]

[tex]\mathbf{C = (2.3)}[/tex] --- the midpoint

The midpoint of a segment is calculated as:

[tex]\mathbf{C = \frac{1}{2}(x_1 + x_2,y_1+y_2)}[/tex]

So, we have:

[tex]\mathbf{(2,3) = \frac{1}{2}(-1 + x,-5+y)}[/tex]

Multiply through  by 2

[tex]\mathbf{(4,6) = (-1 + x,-5+y)}[/tex]

By comparison:

[tex]\mathbf{-1 + x =4}[/tex]

[tex]\mathbf{-5+ y =6}[/tex]

So, we have:

[tex]\mathbf{-1 + x =4}[/tex]

[tex]\mathbf{x = 4 + 1}[/tex]

[tex]\mathbf{x = 5}[/tex]

[tex]\mathbf{-5+ y =6}[/tex]

[tex]\mathbf{y = 6 + 5}[/tex]

[tex]\mathbf{y = 11}[/tex]

Hence, the coordinates of B is (5,11)

Read more about midpoints at:

https://brainly.com/question/13133371

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