Question

Four points A(6,3) , B(-3,5) , C(4,-2) , and D(x,3x) are given in such a way that area of triangle DBC/area of triangle ABC =1/2. Find x

Answer 1

concept : if $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$ are vertices of a triangle. then, area of this triangle is given by, $\Delta=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)$.

using this concept to find area of triangle ABC and area of triangle DBC.

area of triangle DBC, ar(DBC)=1/2 {x (5+2)-3 (-2-3x)+4 (3x-5)}=1/2 (7x+6+9x+12x-20)=1/2 (28x-14)

=14x-7

hence, ar(DBC) = 14x - 7

now, area of triangle ABC, ar (ABC) = 1/2 {6 (5+2)-3 (-2-3)+4 (3-5)} =1/2(42 + 15 - 8)=49/2

hence, at(ABC) = 49/2

a/c to question,

• ar(DBC)/ar(ABC) = 1/2

or, ar (DBC)/ar (ABC)=1/2

or, (14x-7)/(49/2)=1/2

or, 14x-7=49/4

or, 14x = 49/4 + 7 = (49 + 28)/4

or, 14x=77/4

or, x=11/8

hence, value of x = 11/8

Answer 2

Step-by-step explanation:

pls go through the pics (3 pics) attached...

Hope it helps