Study the following information and answer the given questions Point K is 12m to the West of point G. Point M is 4m to the North of Point K. Point J is 10m to the South of Point L. Point F is 6m to the West of point J. Point G lies exactly between Point L and Point J. Point F is 5m north of point O. Point Q is 18m west of point O.

What is the shortest distance between Point K and Point L?

Question

Study the following information and answer the given questions Point K is 12m to the West of point G. Point M is 4m to the North of Point K. Point J is 10m to the South of Point L. Point F is 6m to the West of point J. Point G lies exactly between Point L and Point J. Point F is 5m north of point O. Point Q is 18m west of point O.

What is the shortest distance between Point K and Point L?

Accepted Answer

**Solution:**

1. Assign coordinates to points for clarity:
   - Let point G be at origin $(0,0)$.
   - Since K is 12 m West of G, $K = (-12, 0)$.

2. Point L and J lie on a vertical line because G is exactly between them:
   - Let $L = (0, y)$ and $J = (0, -y)$ since G is midpoint.
   - The distance between L and J is $2y$.

3. Given J is 10 m South of L, so the vertical distance between L and J is 10 m:
   - Therefore, $2y = 10 ightarrow y = 5$.
   - So, $L = (0, 5)$ and $J = (0, -5)$.

4. Now find the distance between K $(-12, 0)$ and L $(0, 5)$:
   - Using distance formula:
   $$	ext{Distance} = \sqrt{(0 + 12)^2 + (5 - 0)^2} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13 	ext{ m}$$

**Answer:** $13 	ext{ m}$

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