Show that area of the triangle formed by the lines, , and is equal to , where and are the roots of the equation .
Given that, and are the roots of the quadratic equation .
Comparing with the standard form of quadratic equation (sum of the roots) product of the roots(, we get
…………………………. .
……………………………
Adding equation and equation , we get
⇒
Similarly,
⇒
Given equations of line are:
…………….
…………….
…………………
We will solve the above equations to obtain the coordinates of the triangle
On solving eq and , we get
we get coordinate of intersecting point
On solving eq and, we get
coordinate of intersecting point
On solving eq and , we get
we get coordinate
Now the area of triangle when three of its vertices are given
⇒ Area
⇒ Area ……………..
Now substitute the value of and in equation , we get
Area
Thus, area of the triangle formed by the lines, , and is equal to . Hence proved