Question

the vertices of triangle are (2,3)(h-2) and (-3,k). If the centroid of the triangle is at the point(4,-2), then find the value of √(h+k)²+(h+2k)²​

Answer 1

Answer:

√37

Step-by-step explanation:

Centroid = (4, - 2)

=> (2+h-3/3 , 3-2+k/3) = (4, -2)

=> (h-1/3 , k+1/3) = (4, - 2)

=> (h-1)/3 = 4 & (k+1)/3 = -2

=> h = 13 & k = - 7

Hence, h + k = 13 + (-7) = 13-7 = 6

h + 2k = 13+2(-7) = 13-14 = -1

Hence,

√(h+k)² + (h+2k)² = √(6)²+(-1)² = √36+1

= 37

Answer 2

Solution(By Examveda Team)

In Give Question,

A + B = 8 ---- (i)

A + C =13 -----(ii)

B + D = 8 ----(iii)

C - D = 6 ----(iv)

Therefore equation (i) and (iii) are equal

A + B = B + D

=> A = D

Therefore, equation (iv) can be C - A = 6 ----- (v)

Now solving equation (ii) and (v), We Get C = 9.5 and A = 3.5

Put this value of A in equation in (i) B = 4.5 and value of C in equation (iv) we get D = 3.5

A = 3.5

B = 4.5

C = 9.5

D = 3.5

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