Question

. If x – 2y + k = 0 is a median of the triangle whose vertices are A(– 1, 3),

B(0, 4) and C(–5, 2), then find the value of k.

 Hint: median of the triangle means use centroid formula get, x and y value

substitute , find K.​

Answer 1

Answer:

Step-by-step explanation:

A(-1,3)

B (0,4)

C (-5,2)

Medians of a triangle meet at a point known as centroid.

Now we will be finding coordinates of the centroid.

Centroid= (x1+x2+x3 ÷3 , y1+y2+y3÷3)

= (-1+0-5÷3 ,3+4+2÷3)

= (-6/3 , 9/3)

= (-2,3)

Given : eq. of median = x-2y+k=0...........(1)

Since centroid lies on the median

therefore, coordinates of centroid satisfies the eq. of median

hence putting values of x and y from centroid to eq. (1)

we get

-2-2×3+k=0

k = 8

hence, value of k is 8