Question

The area of triangle enclosed by the lines x- y=0, x+y= 0 and y= 4 is equal to : (in square units)​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Sides of the given triangle are}$

$\mathsf{x-y=0,\;x+y=0,\;y=4}$

$\underline{\textbf{To find:}}$

$\textsf{Area of the triangle formed the given lines}$

$\underline{\textbf{Solution:}}$

$\textsf{The vertices of the triangle are obtained by solving the equations}$

$\mathsf{Solving\;x-y=0\;and\;x+y=0\;we\;get\;(0,0)}$

$\mathsf{Solving\;x+y=0\;and\;y=4\;we\;get\;(-4,4)}$

$\mathsf{Solving\;x-y=0\;and\;y=4\;we\;get\;(4,4)}$

$\therefore\mathsf{The\;vertices\;are\;(4,4),(-4,4),(0,0)}$

$\underline{\textsf{Area of the triangle}}$

$\mathsf{=\dfrac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]}$

$\mathsf{=\dfrac{1}{2}[4(4-0)-4(0-4)+0(4-4)]}$

$\mathsf{=\dfrac{1}{2}[16+16]}$

$\mathsf{=\dfrac{1}{2}{\times}32}$

$\mathsf{=16\;square\;units}$

$\underline{\textbf{Find more:}}$

If the points (2a,a),(a,2a) and (a,a) enclose a triangle of area 18 square units. Then the centroid of the triangle is:  

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