Question

A parallelogram is drawn with the lines joining (x1, y2) and (x2, y2) to the origin as adjacent sides. what are the coordinates of the fourth vertex?

Answer 1

Answer:

RD Sharma (2019)

CO ORDINATE GEOMETRY

Question 1 :

On which axis do the following points lie?

(a) P(5, 0)

(b) Q(0−2)

(c) R(−4,0)

(d) S(0,5)

Answer :

According to the Rectangular Cartesian Co-ordinate system of representing a point (x, y),

If then the point lies in the 1st quadrant

If then the point lies in the 2nd quadrant

If then the point lies in the 3rd quadrant

If then the point lies in the 4th quadrant

But in case

If then the point lies on the y-axis

If then the point lies on the x-axis

(i) Here the point is given to be P (5, 0). Comparing this with the standard form of

(x, y) we have

Here we see that

Hence the given point lies on the

(ii) Here the point is given to be Q (0, -−2). Comparing this with the standard form of (x, y) we have

Here we see that

Hence the given point lies on the

(iii) Here the point is given to be R (-4, 0). Comparing this with the standard form of (x, y) we have

Here we see that

Hence the given point lies on the

(iv) Here the point is given to be S (0, 5). Comparing this with the standard form of (x, y) we have

Here we see that

Hence the given point lies on the