Straight Lines · Question 25

Let be a triangle formed by the lines 7x - 6y + 3 = 0, x + 2y - 31 = 0 and 9x - 2y - 19 = 0. Let the point (h, k) be the image of the centroid of in the line 3x + 6y - 53 = 0. Then h2 + k2 + hk is equal to :

1. 47
2. 37
3. 40
4. 36

Answer

(2) 37

Solution

Vertices (solving the lines in pairs):

7x - 6y + 3 = 0 and x + 2y - 31 = 0 (9, 11)

x + 2y - 31 = 0 and 9x - 2y - 19 = 0 (5, 13)

7x - 6y + 3 = 0 and 9x - 2y - 19 = 0 (3, 4)

Centroid G = ( 173, 283 )

Image in 3x + 6y - 53 = 0:

h - 1733 = k - 2836 = -2 (17 + 56 - 53 )9 + 36 = - 89

h = 173 - 83 = 3, k = 283 - 163 = 4

h2 + k2 + hk = 9 + 16 + 12 = 37

Answer: (2)