In ?ABC, the equation of altitudes AM and BN are x + 5y - 3 = 0, x + y - k = 0. If the altitude CL is given by 3x - y - 1 = 0, then k = ______.

Question

In $Δ A B C$ , the equation of altitudes AM and BN are $x + 5 y - 3 = 0$ , $x + y - k = 0$ . If the altitude CL is given by $3 x - y - 1 = 0$ , then $k =$ ______.

Smart Achievers · Accepted Answer

(1)

$Solving the altitudes A M and C L, we get$

$Orthocentre = (\frac{1}{2}, \frac{1}{2})$ $lies on x + y - k = 0$ $\Rightarrow k = 1$

Solution

Q.
In $Δ A B C$ , the equation of altitudes AM and BN are $x + 5 y - 3 = 0$ , $x + y - k = 0$ . If the altitude CL is given by $3 x - y - 1 = 0$ , then $k =$ ______.

Ans.
(1)

$Solving the altitudes A M and C L, we get$

$Orthocentre = (\frac{1}{2}, \frac{1}{2})$ $lies on x + y - k = 0$ $\Rightarrow k = 1$

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Solution

Q. In ΔABC, the equation of altitudes AM and BN are x+5y-3=0, x+y-k=0. If the altitude CL is given by 3x-y-1=0, then k= ______.

Ans. (1) Solving the altitudes AM and CL, we get Orthocentre=(12,12) lies on x+y-k=0⇒k=1

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Q.
In $Δ A B C$ , the equation of altitudes AM and BN are $x + 5 y - 3 = 0$ , $x + y - k = 0$ . If the altitude CL is given by $3 x - y - 1 = 0$ , then $k =$ ______.

Ans.
(1)

$Solving the altitudes A M and C L, we get$

$Orthocentre = (\frac{1}{2}, \frac{1}{2})$ $lies on x + y - k = 0$ $\Rightarrow k = 1$