In the given figure, A B C D is a rhombus with diagonals A C = 16 cm and B D = 8 cm . Find the coordinates of A , B , C and D .

Given, A B C D is a rhombus with diagonals A C = 16 cm and B D = 8 cm . We know, The diagonals of a rhombus bisect each other at right angles. Thus, we get: A C = A O + O C = 16 cm ⇒ A O = O C = 8 cm And, B D = B O + O D = 8 cm ⇒ B O = O D = 4 cm Therefore, we get the coordinates according to their corresponding quadrants as follows: A lies on the negative direction of x - axis and the coordinates are - 8 , 0 B lies on the positive direction of y - axis and the coordinates are 0 , 4 C lies on thepositive direction of x - axis and the coordinates are 8 , 0 D lies on the negative direction of y - axis and the coordinates are 0 , - 4 Hence, the points are A - 8 , 0 , B 0 , 4 , C 8 , 0 and D 0 , - 4 .

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Mathematics Textbook of Competency Based Questions for Class IX>Chapter 3 - Coordinate Geometry>Exercise>Q 64

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In the rectangular coordinate system given below, the shaded region is bounded by two straight lines. Which of the following is not an equation of one of the boundary lines?

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Important Questions on Coordinate Geometry

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Mathematics Textbook of Competency Based Questions for Class IX>Chapter 3 - Coordinate Geometry>Exercise>Q 65

In the given figure,

A B C D

is a rhombus with diagonals

A C = 16 cm

and

B D = 8 cm

.

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Find the coordinates of $A, B, C$ and $D$ .

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Mathematics Textbook of Competency Based Questions for Class IX>Chapter 3 - Coordinate Geometry>Exercise>Q 67

In a $100 m$ Race, a stopwatch was used to find the time that it took a group of students to run $100 m$ .

Time (in sec.)	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
No. of students	$8$	$10$	$13$	$6$	$3$

Based on the above information, answer the following question.

The sum of lower limits of median class and modal class is

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Mathematics Textbook of Competency Based Questions for Class IX>Chapter 3 - Coordinate Geometry>Exercise>Q 68

Points

(1, - 1), (2, - 2), (4, - 5), (- 3, - 4)

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Mathematics Textbook of Competency Based Questions for Class IX>Chapter 3 - Coordinate Geometry>Exercise>Q 69

In the given figure,

△ A B C

and

△ A B D

are equilateral triangles. Find the coordinates of points

C

and

D

.

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Mathematics Textbook of Competency Based Questions for Class IX>Chapter 3 - Coordinate Geometry>Exercise>Q 70

Let $A (4, 2)$ , $B (6, 5)$ and $C (1, 4)$ be the vertices of $∆ A B C$ .

(i) The median from A meets BC at D. Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP:PD=2:1
(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ:QE=2:1 and CR:RF=2:1.
(iv) What do yo observe?

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Mathematics Textbook of Competency Based Questions for Class IX>Chapter 3 - Coordinate Geometry>Exercise>Q 71

In which quadrant do the following points lie?