// //]]>
##### Get a free home demo of LearnNext

Available for CBSE, ICSE and State Board syllabus.
Call our LearnNext Expert on 1800 419 1234 (tollfree)
OR submit details below for a call back

clear

Next time you have a doubt while studying, you know where to go. By simply posting your questions on Question & Answer Forum, you can have them answered by academic experts. You can also find related videos and explanations for better understanding.

To find 4th vertex of a parallelogram

Given three of vertices of a parallelogram are A(1,2), B (4,3), C (6,6).

Let the coordinates of fourth vertex be D (x, y)

In a parallelogram, diagonals bisect each other.

He

...

Feb 11

• 4 Likes
• 81531 Views

Feb 11

Find the point on the x-axis which is equidistant from (2,-5) and (-2,9)

Let the point of x-axis be P(x, 0)
Given A(2, -5) and B(-2, 9) are equidistant from P
That is PA = PB
Hence PA 2 = PB 2  → (1)
Distan...

Dec 25

• 3 Likes
• 67340 Views

Dec 25

Syeda answered 1 year(s) , 11 month(s) ago

Ratio in which the line segment joining two points divided by x-axis

Let the point on X-axis be since the y-coordinate is always zero on X-axis.

Given A(2, 3) and B(5, 6)

Let P divides the line segment joining the points (2, 3) and (5, 6) in the ra

...

Feb 11

• 1 Like
• 55924 Views

Feb 11

If two vertices of an equilateral triangle be (0,0), (3,√3), find the third vertex.

Two vertices of an equilateral triangle are (0, 0) and (3, √3).

Let the third vertex of the equilaterla triangle be (x, y)

Distance between (0, 0) and (x,...

Dec 21

• 4 Likes
• 50657 Views

Dec 21

Find the coordinates of the points of trisection of the line segment joining the points.

Sol:

Given line segment joining the points A(1,-2)and B(-3,4)

Let P and Q be the points of trisection of AB i.e., AP = PQ = QB

Therefore, P divides AB internally in the ratio 1 : 2.<

...

Dec 21

• 2 Likes
• 49410 Views

Dec 21

Find the third vertex of the equilateral triangle.

Sol:
Two vertices of an equilateral triangle are (3, 4) and (-2, 3)
Let the third vertex of the triangle be (x, y)
Distance between (3, 4) and (-2, 3)
=√[(-2-3) 2 + (...

Oct 28

• 2 Likes
• 39989 Views

Oct 28

Ramesh answered 4 year(s) , 3 month(s) ago

If a point(x,y) is equidistant from the points (a+b, b-a) & (a-b, a+b), then prove bx = ay.

Distace between the points (x, y) and   (a+b, b-a) & (a-b, a+b) is equal

⇒ √{[x - (a + b)] 2 + [y - (b -a)] 2} = √{x - (a - b)] 2  + [y - (a + b)] 2...

Mar 9

• 4 Likes
• 35137 Views

Mar 9

Find the coordinates of the circumcentre of the triangle.

Let the coordinates of the circumcentre of the triangle be (x, y).
Circumcentre of a triangle is equidistant from each of the vertices.

Distance between (8, 6) an...

Dec 21

• 6 Likes
• 34730 Views

Dec 21

Agam answered 1 year(s) , 10 month(s) ago

If the points A(4, 3) and B(x, 5) lie on the circle

Given centre of circle is O(2, 3)
Points on the circle are A(4, 3) and B(x, 5)
Recall the distance between two points formula�

Squaring on both the...

Nov 15

• 2 Likes
• 28176 Views

Nov 15

Syeda answered 1 year(s) , 11 month(s) ago

what point on x axis is equidistant from the points A(7,6) and B(-3,4) ?

Given points  A(7,6) and B(-3,4)
Let the point be P(x,0) [we know that point on x-axis is (x,0)]
So, AP=PB and AP 2=PB 2
⇒(x-7) 2...

Feb 20

• 5 Likes
• 27283 Views

Feb 20

Ramesh answered 4 year(s) , 5 month(s) ago

Prove that the given points are the vertices of a parallelogram.

Let the points (4, 5) (7, 6) (4, 3) (1, 2) represent the points A, B, C and D.

AB = √[(7 - 4) 2 + (6 - 5) 2] = √(9 + 1) = √10
BC = √[(4 - 7) 2 + (3 -...

Jan 7

• 1 Like
• 20100 Views

Jan 7

Agam answered 1 year(s) , 10 month(s) ago

Coordinates of points of trisection

Solution:

Given coordinates are� �and�
Trisection means dividing a line segment in three equal parts or dividing a line segment� in the ratio 1:2 and 2:1 internally.
Case (i):...

Dec 11

• 2 Likes
• 20029 Views

Dec 11

Raghunath answered 4 year(s) , 4 month(s) ago

Show that the points (a,b+c), (b,c+a), (c,a+b) are collinear.

Any two points of sum is equal to the third then it must be a collinear.

Feb 8

• 0 Like
• 19952 Views

Feb 8

Agam answered 1 year(s) , 10 month(s) ago

Q--- Find the value of k if the points A(2,3) ,B(4,k) and C(6,-3) are collinear.

Given that A, B and C are collinear Hence ar(DABC) = 0

Dec 18

• 1 Like
• 18358 Views

Dec 18

Agam answered 1 year(s) , 8 month(s) ago

Midpoints of triangle are given find its sides

Let the vertices of the triangle are A(x1, y1), B(x2, y2), C(x3, y3)
Draw DE, DF, FE and BF
��

As D and F are mid points of AB and AC
∴�DF || BE
E and F are mi...

Feb 29

• 1 Like
• 16429 Views

Feb 29

Raghunath answered 4 year(s) , 3 month(s) ago

How to derive the section formula?

Consider any two points A ( x 1, y 1) and B ( x 2, y 2) and assume that P ( x, y) divides AB internally in the rat...

Feb 12

• 1 Like
• 15772 Views

Feb 12

Ramesh answered 5 year(s) , 2 month(s) ago

Vertices of an isosceles right angled triangle.

Sol:
Vertices of the triangle are A(-3, 0), B(1, -3), C(4, 1)
Distance between two points =  (x 2 - x 1) 2+(y 2 - y 1) 2...

Dec 18

• 1 Like
• 14277 Views

Dec 18

Raghunath answered 4 year(s) , 4 month(s) ago

What is the formula for finding collinear points?

Sol:
If the A, B and C are three collinear points then AB + BC = AC or AB = AC - BC or BC = AC - AB.

or

If the area of triangle is zero then the points are called colline...

Jan 20

• 2 Likes
• 14267 Views

Jan 20

Agam answered 1 year(s) , 10 month(s) ago

Line segment divided by the Y-axis

Solution:

Let the point on Y-axis be� ����[Since on Y-axis x-coordinate is zero]
Let the Y-axis divide the given points� �in the ratio� �
Therefore the coordinates of P are giv...

Oct 18

• 1 Like
• 13717 Views

Oct 18

Raghunath answered 4 year(s) , 5 month(s) ago

How to derive the formula of centroid from section formula.

Sol:
Let centroid of the triangle the coordinates of whose vertices are given by A(x1, y1), B(x2, y2) and C(x3, y3) respectively.

...

Dec 14

• 0 Like
• 12602 Views

Dec 14

###### Like NextGurukul? Also explore our advanced self-learning solution LearnNext
Offered for classes 6-12, LearnNext is a popular self-learning solution for students who strive for excellence
Explore
Animated Video
lessons
All India
Test Series
Interactive Video
Experiments
Best-in class
books