Question

Find the area of triangle ABC, whose co-ordinates are A(4, -6), B(3,-2) and
C(5,2) then find the length of the median AD?
​

Answer 1

Answer:

6 units

Step-by-step explanation:

to to find the length of the median AD,

we have to use midpoint formula and distance formula.

first we will use midpoint formula

that is,

(x1+x2 , y1+y2) = (3+5 , -2+2) = ( 8 , 0 )

( 2. 2. ) ( 2. 2. ). (. 2. 2 )

= ( 4, 0)

now we will use distance formula

that is ,

= ✓(x2-x1)^2 + (y2-y1)^2

= ✓( 4-4 )^2 + [0-(-6)]^2

= ✓(0)^2 + (6)^2

=✓36

= ✓6

= 6 units.

Answer 2

✪ Given :-

• Coordinates of A = ( 4 , -6 )
• Coordinates of B = ( 3 , -2 )
• Coordinates of C = ( 5 , 2 )

✪ To Find :-

• Area of the triangle ABC

✪ Solution :-

$\red\bigstar\: \boxed{\bf \green{Area = \frac{1}{2} \bigg[x_1(y_2 - y_3) + x_2(y_3 - y_1) +x_3(y_1 - y_2) \bigg ]}}$

Here

• x₁ = 4
• x₂ = 3
• x₃ = 5
• y₁ = -6
• y₂ = -2
• y₃ = 2

Substitute values in formula :

$\longmapsto \sf Area = \frac{1}{2} \bigg[4(-2-2) + 3(2 + 6) +5( - 6 + 2) \bigg ]$

$\longmapsto \sf Area = \frac{1}{2} \bigg[4(-4) + 3(8) +5( - 4) \bigg ]$

$\longmapsto \sf Area = \frac{1}{2} \bigg[ - 16+24 - 20\bigg ]$

$\longmapsto \sf Area = \frac{1}{2} \bigg[ - 12\bigg ]$

$\longmapsto\boxed{\sf\purple{ Area = - 6 \: {unit}^{2}} }$