Three vertices of a rectangle are (3, 2), (-4, 2) and (-4, 5). Plot these points and find the coordinates of the fourth vertex
Solution:
Given, three vertices of a rectangle are (3, 2), (-4, 2) and (-4, 5)
We have to plot the points and find the coordinates of the fourth vertex.
Let the point (3, 2) be A
The x-coordinate is positive and the y-coordinate is positive
Therefore, the point A lies on the first quadrant
Let the point (-4, 2) be B
The x-coordinate is negative and the y-coordinate is positive
Therefore, the point B lies on the second quadrant
Let the point (-4, 5) be C
The x-coordinate is negative and the y-coordinate is positive
Therefore, the point C lies on the second quadrant
On plotting the points A, B and C
To find the fourth vertex D of the rectangle ABCD
We know that the opposite sides of a rectangle are equal.
So the abscissa of A is equal to abscissa of D
So, abscissa of D = 3
The ordinate of C is equal to ordinate of D
So, ordinate of D = 5
Therefore, the coordinates of D are (3, 5)
✦ Try This: By taking rectangular coordinate axis plot the points 0 (0,0), P (3, 0) and R(O, 4). If OPQR is rectangle, then find coordinates of Q.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 3
NCERT Exemplar Class 9 Maths Exercise 3.4 Sample Problem 1
Three vertices of a rectangle are (3, 2), (-4, 2) and (-4, 5). Plot these points and find the coordinates of the fourth vertex
Summary:
Three vertices of a rectangle are (3, 2), (- 4, 2) and (- 4, 5). On plotting these points, the coordinates of the fourth vertex are (3, 5)
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