As the line passes through (0,0) and (8,2), the equation of the line is x = 4y or x-4y = 0.
Take (8,3) and substitute: we get 8-4*3 = 8 - 12 = -4 < 0 hence above line
Take (8,1) and substitute: we get 8-4*1 = 8 - 4 = 4 > 0 hence below line.

Also, if a point has to be in the shaded region, it has to be in the third quadrant.
ELIMINATE A,B,E. Only options to check are C and D.

D: (-4,-4), substitute: -4 - (4*-4) = -4 +16 = 12 > 0, so below line in third quadrant. Hence eliminate

C: (-4, -0.5), substitute: -4 - (4*-0.5) = -4 + 2 = -2 < 0, so above line in third quadrant. Hence has to be inside the shaded region.

Hence Option C

Question stem should be: Which of the following points is located...

dimmak - IMO the question is correct. "points" is in plural form

But there is just one point that complies. I mean, if you say "are" it would state that there are more than one point that comply with the statement. And because of the essence of the Problem Solving questions, there is just one answer.

Hi,
Could you please tell me if a line passing through the origin has a constant as in the equation of the line y = mx + c is zero meaning c = 0? If that is true, then i understand why the equation of the line in the question will be x-4y=0. Else, could you explain why ?

Thanks

This is how I solved it. The shaded region clearly is in the 3rd Quadrant, so options A, B & E are eliminated.

Since the line passes through the origin, the slope of the line can be determined as follows
2-0 / 8-0 = 1/4

Now, for the point to lie in the shaded region, the slope formed by such point with the point (8,2) has to be less than 1/4, which is the slope of our line.
Now, let's test the points in Options C & D
Option C has (-4, -0.5)
So, slope would be 2-(-0.5) / 8-(-4) = 2.5/12, this is less than 1/4.

Option D has (-4, -4)
So, slope would be 2-(-4) / 8-(-4) = 1/2, this is more than 1/4.

Therefore, our answer is Option C.

slope= y2-y1/x2-x1, using the above diagram we will get our slope as 1/4, thus making the equation of our line as 4y=x or 4y-x=0. If we put put the (-4,-0.5) we get 4*(-0.5)-(-4) = 6, then how are we confirming answer choice C, please explain

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