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?

\\(\bigcirc\\) \\((13, 8)\\)
\\(\bigcirc\\) \\((-1, 12)\\)
\\(\bigcirc\\) \\((4, -2)\\)
\\(\bigcirc\\) \\((8, 3)\\)

Explanation:

Identify given values and target coordinates

Using the Coordinate Geometry knowledge point

$$
LATEXBLOCK0
$$

Apply the midpoint formula

The midpoint \(L\) of segment \(\overline{JK}\) is defined by:

$$ x_m = \frac{x_1 + x_2}{2}, \quad y_m = \frac{y_1 + y_2}{2} $$

Solve for the x-coordinate of K

Substitute the known values into the horizontal midpoint equation:

$$
LATEXBLOCK1
$$

Solve for the y-coordinate of K

Substitute the known values into the vertical midpoint equation:

$$
LATEXBLOCK2
$$

State the final coordinates

The coordinates of point \(K\) are:

$$ K = (13, 8) $$

Answer:

• (A) \((13, 8)\) (Correct answer)
• (B) \((-1, 12)\)
• (C) \((4, -2)\)
• (D) \((8, 3)\)