Plot the points P (1, 0), Q (4, 0) and S (1, 3). Find the coordinates of the point R such that PQRS is a square
Solution:
Given, PQRS is a square
The coordinates of P, Q and S are (1, 0), (4, 0) and (1, 3)
We have to find the coordinates of the point R.
Considering the point P(1, 0)
The x-coordinate is positive and the y-coordinate is 0
Therefore, the point P lies on the x-axis
Considering the point Q(4, 0)
The x-coordinate is positive and the y-coordinate is 0
Therefore, the point Q lies on the x-axis
Considering the point S(1, 3)
The x-coordinate is positive and the y-coordinate is positive
Therefore, the point S lies in the first quadrant
Now plotting the points P, Q and S,
We know that all the sides of a square are equal.
In the given square PQRS, the sides PQ = QR = RS = PS
The abscissa of the point Q is equal to the abscissa of the point R
So, the abscissa of the point R = 4
The ordinate of the point S is equal to the ordinate of the point R
So, the ordinate of the point R = 3
Therefore, the coordinates of R = (4, 3)
✦ Try This: Prove that the points A (0, 1), B(1, 4), C(4, 3) and D(3, 0) are the vertices of a square.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 3
NCERT Exemplar Class 9 Maths Exercise 3.4 Problem 3
Plot the points P (1, 0), Q (4, 0) and S (1, 3). Find the coordinates of the point R such that PQRS is a square
Summary:
(x, y) are called the coordinates of the point whose abscissa is x and the ordinate is y. Plotting the points P (1, 0), Q (4, 0) and S (1, 3) such that PQRS is a square. The coordinates of the point R are (4, 3)
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