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givi [52]
3 years ago
6

Given it's midpoint and one endpoint apply the midpoint formula and solve for x and y midpoint (22,15) endpoint (18,6

Mathematics
1 answer:
Nutka1998 [239]3 years ago
4 0
Midpoint formula

mid of (x1,y1) and (x2,y2) is
( \frac{x2+x1}{2}, \frac{y2+y1}{2})

so

(22,15)=( \frac{18+x1}{2}, \frac{6+y1}{2})
therefor

22=\frac{18+x1}{2}
and
15=\frac{6+y1}{2}

slv each
22=\frac{18+x1}{2}
times both sides by 2
44=18+x1
minus 18 both sides
26=x1

15=\frac{6+y1}{2}
times both sides by 2
30=6+y1
minus 6
24=y1

the other point is (26,24)

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x-5+5= 0+5

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To find the equation we will put the values of x and y in the equations and then check if LHS=RHS.

\large\red{\sf{y=3x-1}}

  • x=1
  • y=9

\begin{gathered}\\ \sf\longmapsto 9=3(1)-1\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9=3-1\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9≠2 \end{gathered}

\large\green{\sf{y=5x+4}}

\begin{gathered}\\ \sf\longmapsto 9=5(1)+4\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9=5+4\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9=9\end{gathered}

\large\blue{\sf{y=-2x-8}}

\begin{gathered}\\ \sf\longmapsto 9=-2(1)-8\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9=-2-8\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9≠10\end{gathered}

\large\pink{\sf{y=6x-8}}

\begin{gathered}\\ \sf\longmapsto 9=6(1)-8\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9=6-8\end{gathered}

\begin{gathered}\\ \sf\longmapsto 9≠-2\end{gathered}

Hence, Option B. y=5x+4 satisfies the system (1,9)

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