@Vikrant-Garg @Dhruv-Agarwal

Answer is 121.

Method 1 by rishabh tyagi

Boundary points are-

(8,9),(9,8),(10,7)..(16,1)==>9 points

(-2,1),(-1,2)...(6,9)==>9 points

(-2,0),(-1,0)...(16,0)==>19 points

(-3,0),(7,10),(17,0)==> 3 points

Total 40

Method 2 by @hemant_malhotra :

|x - 7| + |y| + k =10

12c2= 66

as |x-7| can take -ve values 66 * 2 =132

now subtract cases when x - 7 = 0 so |y| < = 10 so 11 values will be removed so 132-11=121

Method 3 by @hemant_malhotra

|x - 7| + |y| < = 10

let x - 7 > = 0

x-7 + y < = 10

so x + y < = 17

here x > = 7

so put x = 7 + a

so 7 + a + y < = 17

so a + y < = 10

so when a = 0 then y < = 10 so 11 values

when a=1 then y < = 9 so 10 values

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.

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when a = 7 then 4 values

when a = 8 then y < = 2

when a = 9 then y < = 1

so 2 values

when a = 10 then y < = 0 so 1 values

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1 + 2 + 3 ... + 11 = 11 * 6 = 66 values

now when 0 < = x < = 6

so -x + 7 + y < = 10

so -x + y < = 3

y - x < = 3

so y < = x + 3

so when x = 0 then y < = 3 so 4 values

when x = 1 then 5 values

tlll x = 6 where 10 values

so 4 + 5 + 6 + 7 + 8 + 9 + 10 = 49

now when x < 0

so -x + 7 + y < = 10

so -x + y < = 3

so y < = x + 3

when x = -1 then y < = 2 so 3 values

when x = -2 then y < = 1 so 2 values

x = -3 y < = 0 so 1 values so 6 value totall

66 + 49 + 6 = 121 values