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Please help for 50 points (geometry)

Please help for 50 points (geometry)-example-1
User Ilyas
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7.8k points

2 Answers

3 votes

Answer:

A

Explanation:

User Complexity
by
8.2k points
7 votes

Answer:

h = 2

k = 5

Explanation:

Midpoint between two points


\textsf{Midpoint}=\left((x_2+x_1)/(2),(y_2+y_1)/(2)\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)

Given:

  • B = Midpoint = (6, 0)
  • A = (x₁, y₁) = (3h+4, 1-2h)
  • C = (x₂, y₂) = (k-3, k-2)

Substitute the given values into the formula:


\implies (6, 0)=\left((k-3+3h+4)/(2),(k-2+1-2h)/(2)\right)


\implies (6, 0)=\left((k+3h+1)/(2),(k-2h-1)/(2)\right)

Equating the x-values to create an expression for k:


\implies (k+3h+1)/(2)=6


\implies k+3h+1=12


\implies k+3h=11


\implies k=11-3h

Equating the y-values to create an expression for k:


\implies (k-2h-1)/(2)=0


\implies k-2h-1=0


\implies k-2h=1


\implies k=2h+1

Equate the expressions for k and solve for h:


\implies 2h+1=11-3h


\implies 5h=10


\implies h=2

Substitute the found value of h into one of the equations for k and solve for k:


\implies k=2(2)+1


\implies k=4+1


\implies k=5

User Saramgsilva
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