Show that the area of the triangle formed by the lines `y=m_1x+c_1,""""y=m_2x+c_2` and `x=0` is `((c_1-c_2)^2)/(2|m_1-m_2|)`

The area of the triangle whose sides y=m_1 x + c_1 , y = m_2 x + c_2 and x=0 is

Show that the area of the triangle formed buy the lines y=m_1x , y=m_2x\ a n d\ y=c is equal to (c^2)/4(sqrt(33)+sqrt(11))w h e r e\ m_1,\ m_2 are the roots of the equation x ^2+(sqrt(3)+2)x+sqrt(3)-1=0.

If m_1 and m_2 are the roots of the equation x^2-a x-a-1=0 , then the area of the triangle formed by the three straight lines y=m_1x ,y=m_2x , and y=a(a!=-1) is (a^2(a+2))/(2(a+1))ifa >-1 (-a^2(a+2))/(2(a+1))ifa >-1 (-a^2(a+2))/(2(a+1))if-2

The area of the triangle formed by the lines y=a x ,x+y-a=0 and the y-axis is (a) 1/(2|1+a|) (b) 1/(|1+a|) (c) 1/2|a/(1+a)| (d) (a^2)/(2|1+a|)

The orthocentre of the triangle formed by the lines x y=0 and x+y=1 is (a) (1/2,1/2) (b) (1/3,1/3) (c) (0,0) (d) (1/4,1/4)

If m_(1),m_(2) be the roots of the equation x^(2)+(sqrt(3)+2)x+sqrt(3)-1 =0 , then the area of the triangle formed by the lines y = m_(1)x,y = m_(2)x and y = 2 is

Prove that the area of the parallelogram formed by the lines a_1x+b_1y+c_1=0,a_1x+b_1y+d_1=0,a_2x+b_2y+c_2=0, a_2x+b_2y+d_2=0, is |((d_1-c_1)(d_2-c_2))/(a_1b_2-a_2b_1)| sq. units.

The area of the parallelogram formed by the lines y=m x ,y=x m+1,y=n x ,a n dy=n x+1 equals. (|m+n|)/((m-n)^2) (b) 2/(|m+n|) 1/((|m+n|)) (d) 1/((|m-n|))

Prove that (-a,-a/2) is the orthocentre of the triangle formed by the lines y = m_(i) x + a/(m_(i)) , I = 1,2,3, m_(1) m_(2) m_(3) being the roots of the equation x^(3) - 3x^(2) + 2 = 0

Consider the following statements : 1. The distance between the lines y=mx+c_(1) and y=mx+c_(2) is (|c_(1)-c_(2)|)/sqrt(1-m^(2)) . 2. The distance between the lines ax+by+c_(1) and ax+by+c_(2)=0 is (|c_(1)-c_(2)|)/sqrt(a^(2)+b^(2)) . 3. The distance between the lines x=c_(1) and x=c_(2) is |c_(1)-c_(2)| . Which of the above statements are correct ?