Question

Find the area ofa triangle ABC with vertex A(1,-4) and the mid points of the sides through A being (2,-1) and (0,-1).

Answer 1

Heya mate!!

To find the area of the triangle ABC, we first find the coordinates of points B and C.

P(2,-1) is the midpoint of AB.

Midpoint of AB:

x- coordinate = (x1 + x2) / 2

⇒ 2 = (1 + x ) / 2

⇒ 4 = 1 + x

⇒ x = 3

y-coordinate = (y1 + y2) / 2

⇒ -1 = (-4 + y ) / 2

⇒ -2 = -4 + y

⇒ y = 2

Midpoint of AC:

x- coordinate = (x1 + x2) / 2

⇒ 0 = (1 + z ) / 2

⇒ 0 = 1 + z

⇒ z = -1

y-coordinate = (y1 + y2) / 2

⇒ -1 = (-4 + t ) / 2

⇒ -2 = -4 + t

⇒ t = 2

Therefore, B(3,2) and C(-1,2) and we know A(1,-4) already.

Now, we find the area of ΔABC,

Hope it helps u dear✌️✌️