How do you find the coordinates of the other endpoint of a segment with the given endpoint T(-3.5, -6) and the midpoint M(1.5, 4.5)?

pighead73283r
2022-11-20
Answered

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artirw9f

Answered 2022-11-21
Author has **20** answers

Step 1

The formula to find the mid-point of a line segment give the two end points is:

$M=(\frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2})$

Where M is the midpoint and the given points are:

$\left({\begin{array}{cc}{x}_{1}& {y}_{1}\end{array}}\right)$ and $\left({\begin{array}{cc}{x}_{2}& {y}_{2}\end{array}}\right)$

Substituting the information we have gives:

$(1.5,4.5)=(\frac{{-3.5}+{{x}_{2}}}{2},\frac{{-6}+{{y}_{2}}}{2})$

To find ${x}_{2}$ we need to solve this equation:

$1.5=\frac{{-3.5}+{{x}_{2}}}{2}$

$2}\times 1.5={2}\times \frac{{-3.5}+{{x}_{2}}}{2$

$3=\overline{){2}}\times \frac{{-3.5}+{{x}_{2}}}{{\overline{){2}}}}$

$3={-3.5}+{{x}_{2}}$

$3.5+3=3.5{-3.5}+{{x}_{2}}$

$6.5=0+{{x}_{2}}$

$6.5={{x}_{2}}$

${{x}_{2}}=6.5$

To find ${y}_{2}$ we need to solve this equation:

$4.5=\frac{{-6}+{{y}_{2}}}{2}$

$2}\times 4.5={2}\times \frac{{-6}+{{y}_{2}}}{2$

$9=\overline{){2}}\times \frac{{-6}+{{y}_{2}}}{{\overline{){2}}}}$

$9={-6}+{{y}_{2}}$

$9+6=6{-6}+{{y}_{2}}$

$15=0+{{y}_{2}}$

$15={{y}_{2}}$

${{y}_{2}}=15$

The other end point of the segment is: $({6.5},{15})$

The formula to find the mid-point of a line segment give the two end points is:

$M=(\frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2})$

Where M is the midpoint and the given points are:

$\left({\begin{array}{cc}{x}_{1}& {y}_{1}\end{array}}\right)$ and $\left({\begin{array}{cc}{x}_{2}& {y}_{2}\end{array}}\right)$

Substituting the information we have gives:

$(1.5,4.5)=(\frac{{-3.5}+{{x}_{2}}}{2},\frac{{-6}+{{y}_{2}}}{2})$

To find ${x}_{2}$ we need to solve this equation:

$1.5=\frac{{-3.5}+{{x}_{2}}}{2}$

$2}\times 1.5={2}\times \frac{{-3.5}+{{x}_{2}}}{2$

$3=\overline{){2}}\times \frac{{-3.5}+{{x}_{2}}}{{\overline{){2}}}}$

$3={-3.5}+{{x}_{2}}$

$3.5+3=3.5{-3.5}+{{x}_{2}}$

$6.5=0+{{x}_{2}}$

$6.5={{x}_{2}}$

${{x}_{2}}=6.5$

To find ${y}_{2}$ we need to solve this equation:

$4.5=\frac{{-6}+{{y}_{2}}}{2}$

$2}\times 4.5={2}\times \frac{{-6}+{{y}_{2}}}{2$

$9=\overline{){2}}\times \frac{{-6}+{{y}_{2}}}{{\overline{){2}}}}$

$9={-6}+{{y}_{2}}$

$9+6=6{-6}+{{y}_{2}}$

$15=0+{{y}_{2}}$

$15={{y}_{2}}$

${{y}_{2}}=15$

The other end point of the segment is: $({6.5},{15})$

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