Question

Please help I am stuck with this problem for homework. I am in the 6th grade.

Answer 1

`(4,11)`

Step-by-step explanation

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints

it is given by

`M=((x_1+x_2)/(2),(y_1+y_2)/(2))`

then

Step 1

Let

`\begin{gathered} P2=(4,3) \\ M=(4,7) \\ P1=unknown=(x_1,y_1) \end{gathered}`

replace

`\begin{gathered} (4,7)=((x_1+4)/(2),(y_1+3)/(2)) \\ \text{hence} \\ 4=(x_1+4)/(2) \\ and \\ 7=(y_1+3)/(2) \end{gathered}`

Step 2

now, we have to solve for x1 and y1

a)

`\begin{gathered} 4=(x_1+4)/(2) \\ \text{Multiply both sides by 2} \\ 4\cdot2=(x_1+4)/(2)\cdot2 \\ 8=x_1+4 \\ \text{subtrac 4 in both sides} \\ 8-4=x_1+4-4 \\ 4=x_1 \end{gathered}`

b)

`\begin{gathered} 7=(y_1+3)/(2) \\ \text{Multiply both sides by 2} \\ 7\cdot2=(y_1+3)/(2)\cdot2 \\ 14=y_1+3 \\ \text{subtract 3 in both sides} \\ 14-3=y_1+3-3 \\ 11=y_1 \end{gathered}`

therefore, the coordinates of the other end point is

`(4,11)`

I hope this helps you