Question

select the correct answer.
the coordinates of point j are (-7,2), and the midpoint of \overline{jk} is at l(3,5). what are the coordinates of point k?
o a. (8,3)
o b. (13,8)
o c. (4,-2)
o d. (-1,12)

Explanation:

Step1: Recall the mid - point formula

The mid - point formula for two points \(J(x_1,y_1)\) and \(K(x_2,y_2)\) is \(L(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Given \(J(-7,2)\) and \(L(3,5)\), let \(K=(x,y)\).

Step2: Solve for \(x\) coordinate of \(K\)

Using the \(x\) - coordinate part of the mid - point formula \(\frac{-7 + x}{2}=3\).
Multiply both sides by \(2\): \(-7+x = 6\).
Add \(7\) to both sides: \(x=6 + 7=13\).

Step3: Solve for \(y\) coordinate of \(K\)

Using the \(y\) - coordinate part of the mid - point formula \(\frac{2 + y}{2}=5\).
Multiply both sides by \(2\): \(2 + y=10\).
Subtract \(2\) from both sides: \(y = 10-2=8\).

Answer:

B. \((13,8)\)