Question

410
food k if drea of Triangle formed by the points
(10, 2); (-3,-1) and (k, t) is 5 units.
(4,5) one collinear​

Answer 1

Answer:

k = 9

Step-by-step explanation:

Correct Question :-

Find the value of 'k' if the area of the triangle formed by the points (10 , 2) , (-3 , -1) , (k , 1) is 5 sq units.

Given,

Area of the triangle = 5 sq units

A = (10 , 2)

B = (-3 , -1)

C = (k , 1)

To Find :-

Value of 'k'

Formula Required :-

$Area=\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

Solution :-

• x_1 = 10 , y_1 = 2
• x_2 = - 3 , y_2 = - 1
• x_3 = k , y_3 = 1

Area =

$\dfrac{1}{2}|10(-1-1)+-3(t-2)+k(2-(-1))|$

$5=\dfrac{1}{2}|10(-2)+-3(-1)+k(3)|$

$10=|-20+3+3k|$

10 = -17 + 3k

10 + 17 = 3k

27 = 3k

k = 27/3

k = 9

∴ Value of 'k' = 9