Q12 of 20 Page 52

Let us show that the points (–7, 12), (19, 18), (15, –6) and (–11, –12) form a parallelogram when they are joined orderly.

Let us mark the points on a graph sheet and call them A, B, C, D and join the four points in the same order to form a four-sided figure.


A = (- 7, 12)


B = (19, 18)


C= (15, - 6)


D= (- 11, - 12)


We know that slope of a line is given by


Slopes of lines AB, BC, CD and DA are calculated as given below.


Slope (AB)


Slope (BC)


Slope (CD)


Slope (DA)


We see that slope of AB = Slope of CD


And


Slope of BC = Slope of DA


So AB ∥ CD and BC ∥ DA


ABCD is a parallelogram.


More from this chapter

All 20 →
10

Let us write by calculation whether the three points O (0, 0), A(4, 3) and B(8, 6) are collinear.

 11

Let us show that the three points (2, 2), (–2, –2) and are the vertices of an equilateral triangle.

 13

Let us show that the points (2, –2), (8, 4), (5, 7) and (–1, 1) are the vertices of a rectangle.

 14

Let us show that the points (2, 5), (5, 9), (9, 12) and (6, 8) form a rhombus when they are joined orderly.