Question
\( \overline{K L} \) has a midpoint at \( M(-6,-6) \). Point \( K \) is at \( (-3,-3) \). Find the coordinates of point \( L \). Write the coordinates as decimals or integers. \( L=(\square) \)
Ask by Spencer Edwards. in the United States
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Point L is at (–9, –9).
Solution
To find the coordinates of point L, use the midpoint formula. The midpoint M of a segment with endpoints K(x₁, y₁) and L(x₂, y₂) is given by:
M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Given:
M = (–6, –6)
K = (–3, –3)
Let L = (x, y). Then:
(–3 + x) / 2 = –6 and (–3 + y) / 2 = –6
Solve for x:
–3 + x = –12 → x = –12 + 3 = –9
Solve for y:
–3 + y = –12 → y = –12 + 3 = –9
Thus, point L is at:
L = (–9, –9)
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Simplify this solution Beyond the Answer
To find the coordinates of point \( L \), we can use the midpoint formula. The midpoint \( M \) is calculated as follows: \[ M = \left( \frac{x_K + x_L}{2}, \frac{y_K + y_L}{2} \right) \] Given \( M(-6,-6) \) and \( K(-3,-3) \), we can set up the equations: 1. \( \frac{-3 + x_L}{2} = -6 \) 2. \( \frac{-3 + y_L}{2} = -6 \) Now, solving the first equation for \( x_L \): \[ -3 + x_L = -12 \implies x_L = -12 + 3 = -9 \] Now, solving the second equation for \( y_L \): \[ -3 + y_L = -12 \implies y_L = -12 + 3 = -9 \] Thus, the coordinates of point \( L \) are \( L=(-9,-9) \). So, \( L=(-9, -9) \).
