Let the three sides of a triangle are on the lines $4x - 7y + 10 = 0$, $x + y = 5$, and $7x + 4y = 15$. Then the distance of its orthocenter from the orthocenter of the triangle formed by the lines $x = 0$, $y = 0$, and $x + y = 1$ is
Show Hint
- 5
- $\sqrt{5}$
- $\sqrt{20}$
- 20
The Correct Option is B
Solution and Explanation
1. Identify the vertices of the triangle:
- Solve the system of equations to find the intersection points of the lines.
2. Find the orthocenter of the triangle:
- The orthocenter is the intersection of the altitudes.
3. Find the orthocenter of the triangle formed by $x = 0$, $y = 0$, and $x + y = 1$:
- The orthocenter is the intersection of the altitudes.
4. Calculate the distance between the two orthocenters:
- Use the distance formula to find the distance between the two points.
Therefore, the correct answer is (2) $\sqrt{5}$.
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