Let the points of intersection of the lines x | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The intersection points of the given lines are the midpoints of the sides of triangle $ABC$. Let these points be $D(1, 2)$,$E(7, 5)$,and $F(2, 3)$

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(D) The intersection points of the given lines are the midpoints of the sides of triangle $ABC$. Let these points be $D(1, 2)$,$E(7, 5)$,and $F(2, 3)$.The area of the triangle formed by the midpoints $(\Delta DEF)$ is given by:$\Delta DEF = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$$\Delta DEF = \frac{1}{2} |1(5 - 3) + 7(3 - 2) + 2(2 - 5)|$$\Delta DEF = \frac{1}{2} |1(2) + 7(1) + 2(-3)|$$\Delta DEF = \frac{1}{2} |2 + 7 - 6| = \frac{1}{2} |3| = 1.5$The area of the original triangle $ABC$ is $4$ times the area of the triangle formed by joining the midpoints:$	ext{Area}(ABC) = 4 	imes \Delta DEF = 4 	imes 1.5 = 6$.

Let the points of intersection of the lines $x-y+1=0$,$x-2y+3=0$,and $2x-5y+11=0$ be the midpoints of the sides of a triangle $ABC$. Then the area of the triangle $ABC$ is .... .

Similar Questions

If $(4,3)$ and $(1,-2)$ are the end points of a diagonal of a square,then the equation of one of its sides is

One of the vertices of a square is the origin,and the adjacent sides of the square lie along the positive $x$ and $y$ axes. If the side length is $5$,which of the following is $NOT$ a vertex of the square?

The pair of lines $x^2 - 8x + 12 = 0$ and $y^2 - 14y + 45 = 0$ form a square. What is the center of the circle inscribed in the square?

The equations of the sides of a triangle are $x - 3y = 0$,$4x + 3y = 5$,and $3x + y = 0$. The line $3x - 4y = 0$ passes through:

The area of the triangle formed by the lines $y = m_1x + c_1$,$y = m_2x + c_2$ and $x = 0$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module