Question

find the area of a triangle ABC with A(1,-4) and mid points of sides through A being (2,-1) and (0,-1)

Answer 1

please find the attachment

Answer 2

Answer:

12 sq.units

Step-by-step explanation:

REFER TO THE ATTACHMENT FOR DIAGRAM........

☆ Coordinates of D :

D(2,-1) = D[(a+1)/2 + (b-4)/2]

By comparing coordinates:

▪ 2 = (a+1)/2

2*2 = a+1

4 = a+1

a = 3

▪ -1 = (b-4)/2

-1*2 = b-4

-2 = b-4

b = 2

Therefore, coordinates of B are B(3,2).

☆ Coordinates of E :

E(0,-1) = E[(c+1)/2 + (d-4)/2]

By comparing coordinates :

▪ 0 = (c+1)/2

2*0 = c+1

c+1 = 0

c = -1

▪ -1 = (d-4)/2

-1*2 = d-4

-2 = d-4

d = 2

Therefore, coordinates of C are C(-1,2).

☆ In triangle ABC:

A(1,-4)

B(3,2)

C(-1,2)

☆ Let :

x1 = 1

y1 = -4

x2 = 3

y2 = 2

x3 = -1

y3 = 2

☆ Area of triangle ABC = 1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]

= 1/2[1(2-2)+3(2+4)-1(-4-2)]

= 1/2[1(2-2)+3(2+4)-1(-4-2)]

= 1/2[1(0)+3(6)-1(-6)]

= 1/2(0+18+6)

= 1/2(24)

= 12 sq.units

HOPE THIS ANSWER WILL HELP YOU......

Mark as brainliest......

# jasleenlehri13..........