Question

find the area of the triangle abc with the coordinates of a as (1,-4) and the coordinates of the mid points of sides ab and ac respectively are (2,-1) and (0,-1).​

Answer 1

Answer:

13.40

Step-by-step explanation:

By using formula to find midpoint

midpoint = (xB + x1) / 2

2 = xB + 1 / 2

4 = xB + 1

xB = 3

midpoint = (xC + x1) / 2

0 = xC + 1 / 2

0 = xC + 1

xC = -1

midpoint = (yB + y1) / 2

-1 = yB + (-4) /2

-2 = yB - 4

yB = 2

midpoint = (yC + y1) / 2

-1 = yC +(-4) /2

-2 = yC - 4

yC = 2

so now

A (1,-4)

B (3,2)

C (-1,2)

distance of base AB = √(x2-x1)² + (y2-y1)²

                                  = √(3-1)² + (2+4)²

                                  = √ (2)²+(6)²

                                  = 6.32

distance of base height C and midpointAB

= √(x2-x1)² + (y2-y1)²

= √(-1-2)² + (2 + 1)²

= √ 9 + (3)²

= √18

= 4.24

 

Area of triangle = 1/2 (base ) (height)

                          = 1/2(4.24)(6.32)

                         = 13.40