CONNECT POINTS IN CARTESIAN PLANE AND MAKE FIGURE

Sometimes, when you connect points, they make a figure, like a square, rectangle, triangle, etc.! 

If the question requires to find area or perimeter of the shape created by connecting all the points, we have to use the formulae given below.

Rectangle :

Area = length x width

Perimeter = 2(length + width)

Square :

Area = Side x side

Perimeter = 4 (side)

Triangle :

Area = (1/2) x base x height

Perimeter = Sum of lengths of all sides

Problem 1 :

a) Plot the following points on the grid below :

A(3, 2), B(-3, 2),C(-3, -2), and D(3, -2).

b) Now, connect them.

c) What kind of shape do they make ?

d) Can you find the area of this figure ?

Solution :

a) Given points A(3, 2), B(-3, 2),C(-3, -2), and D(3, -2).

b)

c) The shape is rectangle.

d) area of the rectangle = l × w

= 6 × 4

= 24 unit²

Problem 2 :

a) Plot the following points on the grid below : A(4, 1), B(1, 5), and C(-2, 1).

b) Now, connect them.

c) What type of polygon do they make ?

d) Find the area of this figure ?

Solution :

a)  Given points A(4, 1), B(1, 5), and C(-2, 1).

b)

c) The type of polygon is triangle.

d) area of the triangle = 1/2 (b × h)

= 1/2 (6 × 4)

= 1/2 (24)

 = 12 unit²

Problem 3 :

Graph the points A(1, 1), B(5, 1), C(5, 4). What must be the coordinates of of point D if ABCD is a rectangle ?

D( , )

Solution :

Given points A(1, 1), B(5, 1), C(5, 4)

So, the missing point is (1, 4).

Problem 4 :

Graph the points P(-2, -4) and Q(2, -4). What are the coordinates of R and S if PQRS is a square ? (Two answers are possible).

R(__, __)

S(__, __)

Solution :

Given points P(-2, -4) and Q(2, -4).

So, the missing point is (2, 0) and (-2,0).

Problem 5 :

a) Graph and connect the given points : A(1, 7), B(1, 2),and C(5, 2).

b) Identify the figure (shape) :

c) Find the area of the figure :

Solution :

a)

b) The figure shape is right triangle.

c)  The area of the right triangle  = (1/2) x base x height

= (1/2) x 4 x 5

= 20/2

= 10 unit²

Problem 6 :

a)Graph and connect the given points :

P(-1, 3), Q(5, 3), R(5, -2), and S(-1, -2).

b) Identify the figure (shape) :

c) Find the area of the figure :

Solution :

a) 

b) The figure shape is rectangle.

c)   area of the rectangle = l × w

= 6 × 5

= 30 unit²