Question

Please help for 50 points (geometry)

Answer 1

A

Explanation:

Answer 2

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`