Question

Write the coordinates of any point p in the fourth quadrant which is equidistant from the two axes.

Answer 1

If you plot a graph with standard equation of straight line i.e., y=mx+c.
Then you'll get to know that the condition given by ques is y=x.
Which is possible only if slope of the line (m) = 1 and y-intercept (c) =0 then only you'll see y=x.
This implies, m= tan 45°.If we plot a line subtending 45° angle to both x as well as y axes. The line we get will fulfill the given condition.

Answer 2

Let the point P be ( x, y)

Distance from the Y-axis is X-coordinate

Distance from the X-axis is Y-Coordinate .

P is in the fourth quadrant, so X coordinate is positive and Y coordinate is negative.

x = x. y = -y.

Also, The point P is equidistant from both axis .

Distance from X-axis = Distance from Y-axis

X coordinate = Y coordinate .

So, x = y .

Now, the point P is ( x, -x) such that x is non negative .

P = { ( x, -x) / x ∈ R+ }