The equation of sides of a triangle are $7 x - 5 y - 11 = 0, 8 x + 3 y + 31 = 0, x + 8 y - 19 = 0 .$ Then the point (0,0) lies

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inside of triangle

outside of triangle

on the triangle

can't say

answer is A.

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Detailed Solution

We check the sign of each line when we substitute (0,0). If the signs do not match the triangle's orientation, the point lies outside.

Given side equations

7x - 5y - 11 = 0

8x + 3y + 31 = 0

x + 8y - 19 = 0

Step 1 - Substitute the point (0,0)

Line	Expression value at (0,0)	Sign
7x - 5y - 11	-11	Negative
8x + 3y + 31	31	Positive
x + 8y - 19	-19	Negative

Step 2 - Interpret the signs

For a point to be inside a triangle, its sign (positive or negative) when substituted into each side's equation must match the sign of the triangle region for that side. Here, the signs are negative, positive, negative — they are not all the same or consistent with one orientation.