The line (x+y=0) must pass through which point?
Answer and explanation
Correct answer: ((0,0))
The governing test is direct substitution: a point lies on a line if its coordinates make the equation true. For the origin (0,0), x+y=0+0=0, so the equation is satisfied and the line must pass through that point. Therefore option C is correct. Checking the distractors confirms the result: (1,1) gives 2, (0,1) gives 1, and (1,0) gives 1; none of these equals 0. In fact, x+y=0 can also be written as y=−x, a line through the origin with slope −1. The phrase “must pass” asks for a guaranteed point, and the origin is guaranteed by the zero constant term.
Frequently asked questions
What is the correct answer to this question?
((0,0))
Why is this the correct answer?
The governing test is direct substitution: a point lies on a line if its coordinates make the equation true. For the origin (0,0), x+y=0+0=0, so the equation is satisfied and the line must pass through that point. Therefore option C is correct. Checking the distractors confirms the result: (1,1) gives 2, (0,1) gives 1, and (1,0) gives 1; none of these equals 0. In fact, x+y=0 can also be written as y=−x, a line through the origin with slope −1. The phrase “must pass” asks for a guaranteed point, and the origin is guaranteed by the zero constant term.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
