Question

If the area of the triangle formed by the points (10, 2), (-3, -4) and (x, 1) is 5 square units,
then the value of x is​

Answer 1

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

$\textsf{Area of the triangle formed by the points (10,2), (-3,-4) and}$

$\textsf{(x,1) is 5 square units}$

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

$\textsf{The value of 'x'}$

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

$\textsf{Area of the triangle = 5 square units}$

$\implies\mathsf{\dfrac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]=5}$

$\implies\mathsf{\dfrac{1}{2}[10(-4-1)+(-3)(1-2)+x(2+4)]=5}$

$\implies\mathsf{\dfrac{1}{2}[10(-5)+(-3)(-1)+x(6)]=5}$

$\implies\mathsf{\dfrac{1}{2}[-50+3+6x]=5}$

$\implies\mathsf{-47+6x=10}$

$\implies\mathsf{6x=10+47}$

$\implies\mathsf{6x=57}$

$\implies\boxed{\mathsf{x=\dfrac{57}{6}}}$

$\underline{\textbf{Answer:}}$

$\mathsf{The\;value\;of\;x\;is\;\dfrac{57}{6}}$

$\underline{\textbf{Concept used:}}$

$\boxed{\begin{minipage}{7cm} \\\mathsf{Area\;of\;the\;triangle\;formed\;by\;the\;points}\\\\\mathsf{(x_1,y_1),\;(x_2,y_2)\;and\;(x_3,y_3)\;is}\\\\\mathsf{\dfrac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]}\\ \end{minipage}}$

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

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:

https://brainly.in/question/9522665

Area of ​​a triangle formed by x-axis, y-axis and line x + y = 8 is ....... square unit

https://brainly.in/question/14901491

Answer 2

I hope this will help you!