Question

Which of the following could be the points that Jamur plots?

Answer 1

To solve this problem, we need to calculate the midpoint for the two points in each option and check if it corresponds to the given midpoint (-3,4).

Calculating the midpoint for the two points of option A.

We have the points:

`(-1,7)and(2,3)`

We label the coordinates as follows:

`\begin{gathered} x_1=-1 \\ y_1=7 \\ x_2=2 \\ y_2=3 \end{gathered}`

And use the midpoint formula:

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

Substituting our values:

`(\frac{-1_{}+2_{}}{2},\frac{7_{}+3_{}}{2})`

Solving the operations:

`(\frac{1_{}}{2},\frac{10_{}}{2})=(\frac{1_{}}{2},5)`

Since the midpoint is not the one given by the problem, this option is not correct.

Calculating the midpoint for the two points of option B.

We have the points:

`(-2,6)and(-4,2)`

We follow the same procedure, label the coordinates:

`\begin{gathered} x_1=-2 \\ y_1=6 \\ x_2=-4 \\ y_2=2 \end{gathered}`

And use the midpoint formula:

`\begin{gathered} ((x_1+x_2)/(2),(y_1+y_2)/(2)) \\ \text{Substituting our values} \\ (\frac{-2-4_{}}{2},\frac{6+2_{}}{2}) \\ \text{Solving the operations:} \\ ((-6)/(2),(8)/(2)) \\ (-3,4) \end{gathered}`

The midpoint for the two points in option B is (-3,4) which is the midpoint given by the problem.

Answer: B (-2,6) and (-4,2)