Question

find the area of the triangle formed by joining the mid points of the sides of the triangle whose vertices are (0,1),(2,1),(0,3).Find the ratio of this area to the area of the given triangle

Answer 1

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Answer 2

Answer:

$\text{Area of FED}=\frac{1}{2}$ square unit.

The ratio of the ar(DEF) to the ar(ABC) is 1:4

Step-by-step explanation:-

The vertices of a triangle are A(0,1) B(2,1) and C(0,3).

Let,

D is mid point of AB

E is mid point of BC

F is mid point of AC

Mid Point formula: $(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})$

$\text{Coordinate of D}=(\dfrac{0+2}{2},\dfrac{1+1}{2})\Rightarrow (1,1)$

$\text{Coordinate of E}=(\dfrac{0+2}{2},\dfrac{1+3}{2})\Rightarrow (1,2)$

$\text{Coordinate of F}=(\dfrac{0+0}{2},\dfrac{1+3}{2})\Rightarrow (0,2)$

Now we will find the area of triangle DEF.

$\text{Area of FED}=\dfrac{1}{2}|1(2-2)+1(1-2)+0(1-2)|\Rightarrow \dfrac{1}{2}$

$\text{Area of ABC}=\dfrac{1}{2}|0(1-3)+2(1-3)+0(1-1)|\Rightarrow 2$

The ratio of the ar(DEF) to the ar(ABC) is (1/2):2 = 1:4

Hence, The area of triangle DEF is 1/2 square unit and ratio of area 1:4