Question

if the distance between the points (1, 2) & (2, 7) is double ofcthe distance of point (k+4, k) from the origin then value of 8k^2+32k+49 is ...............?


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Answer 1

Answer:

2

Step-by-step explanation:

Using distance formula, The distance between points (1,2) & (2,7)

= root of [ (2-1)^2 + (7-2)^2 ]

= root 26.

The distance between (0,0) & (k+4,k) is half of root 26.

(root 26)/2 = root of [ (k+4)^2 + k^2 ]

taking squares both sides,

26/4 = k^2 + 8k + 16 + k^2

2(k^2) + 8k + (38/4) = 0

simplify more, we get

8(k^2) + 32k + 38 =0

we have to find ,

8(k^2) + 32k + 40

= 8(k^2) + 32k + 38 +2  

= 0 + 2

= 2