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Can somone help me find the orthcenter for the triangle with the given vertices M(-4,-2),N(6,-2) and P(-2,10)?
I don't understand the steps you need to take to geth the answer which I know is (-2,-2/3) may somone please help me with the work?
1 Answer
- Φ² = Φ+1Lv 73 years ago
The line passing through P and perpendicular to MN is (6--4)x + (-2--2)y = (6--4)(-2) + (-2--2)10, which simplifies to x = -2.
The line passing through N and perpendicular to PM is (-2--4)x + (10--2)y = (-2--4)6 + (10--2)(-2), which simplifies to x + 6y = -6.
The orthocentre is the intersection of these two lines, which is (-2, -⅔)
Source(s): The equation of the line through (x₀,y₀), perpendicular to the line through (x₁,y₁) and (x₂,y₂) is (x₂-x₁)x + (y₂-y₁)y = (x₂-x₁)x₀ + (y₂-y₁)y₀
