If D, E, and F are the midpoints of the sides | vedclass

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

Question

(B) The area of the triangle formed by joining the midpoints of the sides of a triangle is one-fourth of the area of the original triangle.First,calcu

Vedclass · Accepted Answer

$2.5$

Vedclass · Answer

(B) The area of the triangle formed by joining the midpoints of the sides of a triangle is one-fourth of the area of the original triangle.First,calculate the area of $\Delta ABC$ using the coordinates $A(5, -1), B(-7, 6),$ and $C(1, 3)$.Area of $\Delta ABC = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$$= \frac{1}{2} |5(6 - 3) + (-7)(3 - (-1)) + 1(-1 - 6)|$$= \frac{1}{2} |5(3) - 7(4) + 1(-7)|$$= \frac{1}{2} |15 - 28 - 7|$$= \frac{1}{2} |-20| = 10 	ext{ sq. units}$.Since the area of $\Delta DEF = \frac{1}{4} 	imes 	ext{Area of } \Delta ABC$,Area of $\Delta DEF = \frac{1}{4} 	imes 10 = 2.5 	ext{ sq. units}$.

If $D, E,$ and $F$ are the midpoints of the sides $AB, BC,$ and $CA$ of the triangle formed by the points $A\ (5, -1), B\ (-7, 6),$ and $C\ (1, 3)$ respectively,find the area of $\Delta DEF$.

Similar Questions

The area (in square units) of the triangle formed by the points with polar coordinates $(1, 0)$,$(2, \frac{\pi}{3})$,and $(3, \frac{2\pi}{3})$ is:

Find the area of the pentagon with vertices $A(1, 1)$,$B(7, 21)$,$C(7, -3)$,$D(12, 2)$,and $E(0, -3)$.

If $(1, 1)$,$(3, 4)$,$(5, -2)$,and $(4, -7)$ are the vertices of a quadrilateral,find its area.

$A$ rectangle is divided into $16$ sub-rectangles as shown in the figure. The number in each sub-rectangle represents its area. What is the area of the rectangle $KLMN$?

Draw a quadrilateral in the Cartesian plane,whose vertices are $(-4, 5), (0, 7), (5, -5),$ and $(-4, -2).$ Also,find its area.

Vedclass Test Series

Exam Paper Generator

Online Exam Module