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) and (0,3). Find the ratio of this area to the area of the
given triangle​

Answer 1

Answer:

Step-by-step explanation:

i will say trick for both finding vertices from mid points and area

first draw triangle

take mid points as down ,right,left like this

                                 

                    0,3                          2,1

                                    0,-1

add 0,3 and 2,1 and subtract  0,-1

you will get  2,5

which is vertice opposite to 0,-1

the midpoint of 0,-1 and another vertice is  0,3

the midpoint  o 0,-1 and another vertice is 2,1

on solving you get vertices as

0,7(left) , (4,3) right

therefore vertices  0,-1 ,   0,7 , 4,3

for area trick is

write coordinates as it is

0,-1    0,7     4,3

add any coordinate to its additive inverse

0,-1     0,7       4,3

0,1        0,1        0,1

add up and down points you get

0 0       0 8       4 4

now take 0 8   4  4

now multiply inner with inner and outer with outer

do     outer product - inner product

here it is 32

half it

you get 16 which is your answer