In the rectangle shown below, the sides are parallel to the axes and the origin is the midpoint: What are the coordinates of other three vertices?

Given: A B C D is a rectangle, C 3 , 2 and O ( 0 , 0 ) . Since, C is in first quadrant, so both the coordinates are positive. D is in second quadrant so value of x will be negative and value of y will be positive. So D ' s coordinates are ( - 3 , 2 ) . A is in third quadrant so value of x & y will be negative. So A ' s coordinates are ( - 3 , - 2 ) . B is in fourth quadrant so value of x will be positive and value of y will be negative. So B ' s coordinates are ( 3 , - 2 ) . Hence, the coordinates of three vertices are A ( - 3 , - 2 ) , B ( 3 , - 2 ) & D ( - 3 , 2 ) .

The triangle shown below is equilateral: Find the coordinates of its vertices.

Given: A B O is an equilateral triangle and O B = 4 Since O B = 4 therefore, a perpendicular line from A on line O B bisects O B . So, O D = 4 2 = 2 O B = O A = A B = 4 (Equilateral triangle) By using Pythagoras theorem; A D 2 = O A 2 - O D 2 ⇒ A D 2 = 4 2 - 2 2 ⇒ A D = 16 - 4 ⇒ A D = 12 ⇒ A D = 2 3 = 2 × 1 . 732 = 3 . 464 Hence, the coordinates of three vertices of triangle are A ( 2 , 3 . 464 ) , O ( 0 , 0 ) & B ( 4 , 0 )

A large trapezium made up of four equal trapeziums. Find the coordinates of the vertices of all these trapeziums.

In trapezium (1). Coordinates of the vertices are ( 0 , 0 ) , ( 2 , 2 ) , ( 4 , 2 ) , ( 4 , 0 ) In trapezium (2). Coordinates of the vertices are ( 4 , 0 ) , ( 4 , 2 ) , ( 6 , 2 ) , ( 8 , 0 ) In trapezium (3), Coordinates of the vertices are ( 2 , 2 ) , ( 4 , 4 ) , ( 6 , 4 ) , ( 6 , 2 ) In trapezium (4). Coordinates of the vertices are ( 8 , 0 ) , ( 6 , 2 ) , ( 6 , 4 ) , ( 8 , 4 )

E M B I B E

Standard 10 Mathematics Part - 1>Chapter 6 - Coordinates>Exercise 1

Kerala Board Solutions for Chapter: Coordinates, Exercise 1: Exercise 1

Author:Kerala Board

Kerala Board Mathematics Solutions for Exercise - Kerala Board Solutions for Chapter: Coordinates, Exercise 1: Exercise 1

Attempt the free practice questions on Chapter 6: Coordinates, Exercise 1: Exercise 1 with hints and solutions to strengthen your understanding. Standard 10 Mathematics Part - 1 solutions are prepared by Experienced Embibe Experts.