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class 10
| math
| coordinate geometry
Solutions for all the questions from class 10
of subject math
of chapter coordinate geometry
CLASS
11
12
class 10
class 11
class 12
class 13
class 6
class 7
class 8
class 9
SUBJECT
math
CHAPTER
area related to circles
areas related to circles
arithmetic progressions
circles
constructions
control and coordination
coordinate geometry
heron's formula
introduction to trigonometry
limits and derivatives
View All ↓
Class 10
Math
All topics
Coordinate Geometry
You have studied in Class IX, that a median of a triangle divides it into two triangles of equal areas. Verify this result for
$ΔABC$
whose vertices are
$A(4,−6),B(3,−2)$
and
$C(5,2)$
.
Class 10
Math
All topics
Coordinate Geometry
The Class
$X$
students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmoharare planted on the boundary at a distance of
$1$
m from each other. There is a triangular grassy lawn in the plot as shown in the Fig. The students are to sow seeds of flowering plants on the
remaining area of the plot.
(i) Taking
$A$
as origin, find the coordinates of the vertices of the triangle.
(ii) What will be the coordinates of the vertices of
$ΔPQR$
if
$C$
is the origin?
Also calculate the areas of the triangles in these cases. What do you observe?
Class 10
Math
All topics
Coordinate Geometry
$ABCD$
is a rectangle formed by the points
$A(−1,−1)$
,
$B(−1,4)$
,
$C(5,4)$
and
$D(5,−1)$
.
$P,Q,R$
and
$S$
are the mid-points of
$AB$
,
$BC$
,
$CD$
and
$DA$
respectively. Is the quadrilateral
$PQRS$
a square? a rectangle? or a rhombus? Justify your answer.
Class 10
Math
All topics
Coordinate Geometry
Determine the ratio in which the line
$2x+y−4=0$
divides the line segment joining the points
$A(2,−2)$
and
$B(3,7)$
.
Class 10
Math
All topics
Coordinate Geometry
Find a relation between
$x$
and
$y$
if the points
$(x,y),(1,2)$
and
$(7,0)$
are collinear.
Class 10
Math
All topics
Coordinate Geometry
The vertices of a
$ΔABC$
are
$A(4,6),B(1,5)$
and
$C(7,2)$
. A line is drawn to intersect sides
$AB$
and
$AC$
at
$D$
and
$E$
respectively, such that
$ABAD =ACAE =41 $
. Calculate the area of the
$ΔADE$
and compare it with the area of
$ΔABC$
.
Class 10
Math
All topics
Coordinate Geometry
The two opposite vertices of a square are
$(−1,2)$
and
$(3,2)$
. Find the coordinates of the other two vertices.
Class 10
Math
All topics
Coordinate Geometry
Let
$A(4,2),B(6,5)$
and
$C(1,4)$
be the vertices of
$ΔABC$
.
(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?
[Note : The point which is common to all the three medians is called the centroid
and this point divides each median in the ratio
$2:1$
.]
(v) If
$A(x_{1},y_{1}),B(x_{2},y_{2})$
and
$C(x_{3},y_{3})$
are the vertices of
$ΔABC$
, find the coordinates of the centroid of the triangle.
Class 10
Math
All topics
Coordinate Geometry
Using the distance formula, show that the given points are collinear.
$(1,−1),(5,2)$
and
$(9,5)$
.
Class 10
Math
All topics
Coordinate Geometry
If the points
$A(4,3)$
and
$B(x,5)$
lie on a circle with the centre
$O(2,3)$
, find the value of x.
1
2
3
4
5
6
7
8
9
10
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class 10
| math
| coordinate geometry
Solutions for all the questions from class 10
of subject math
of chapter coordinate geometry
Filter Results
CLASS
11
12
class 10
class 11
class 12
class 13
class 6
class 7
class 8
class 9
SUBJECT
math
CHAPTER
area related to circles
areas related to circles
arithmetic progressions
circles
constructions
control and coordination
coordinate geometry
heron's formula
introduction to trigonometry
limits and derivatives
View All ↓
Class 10
Math
All topics
Coordinate Geometry
You have studied in Class IX, that a median of a triangle divides it into two triangles of equal areas. Verify this result for
$ΔABC$
whose vertices are
$A(4,−6),B(3,−2)$
and
$C(5,2)$
.
Class 10
Math
All topics
Coordinate Geometry
The Class
$X$
students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmoharare planted on the boundary at a distance of
$1$
m from each other. There is a triangular grassy lawn in the plot as shown in the Fig. The students are to sow seeds of flowering plants on the
remaining area of the plot.
(i) Taking
$A$
as origin, find the coordinates of the vertices of the triangle.
(ii) What will be the coordinates of the vertices of
$ΔPQR$
if
$C$
is the origin?
Also calculate the areas of the triangles in these cases. What do you observe?
Class 10
Math
All topics
Coordinate Geometry
$ABCD$
is a rectangle formed by the points
$A(−1,−1)$
,
$B(−1,4)$
,
$C(5,4)$
and
$D(5,−1)$
.
$P,Q,R$
and
$S$
are the mid-points of
$AB$
,
$BC$
,
$CD$
and
$DA$
respectively. Is the quadrilateral
$PQRS$
a square? a rectangle? or a rhombus? Justify your answer.
Class 10
Math
All topics
Coordinate Geometry
Determine the ratio in which the line
$2x+y−4=0$
divides the line segment joining the points
$A(2,−2)$
and
$B(3,7)$
.
Class 10
Math
All topics
Coordinate Geometry
Find a relation between
$x$
and
$y$
if the points
$(x,y),(1,2)$
and
$(7,0)$
are collinear.
Class 10
Math
All topics
Coordinate Geometry
The vertices of a
$ΔABC$
are
$A(4,6),B(1,5)$
and
$C(7,2)$
. A line is drawn to intersect sides
$AB$
and
$AC$
at
$D$
and
$E$
respectively, such that
$ABAD =ACAE =41 $
. Calculate the area of the
$ΔADE$
and compare it with the area of
$ΔABC$
.
Class 10
Math
All topics
Coordinate Geometry
The two opposite vertices of a square are
$(−1,2)$
and
$(3,2)$
. Find the coordinates of the other two vertices.
Class 10
Math
All topics
Coordinate Geometry
Let
$A(4,2),B(6,5)$
and
$C(1,4)$
be the vertices of
$ΔABC$
.
(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?
[Note : The point which is common to all the three medians is called the centroid
and this point divides each median in the ratio
$2:1$
.]
(v) If
$A(x_{1},y_{1}),B(x_{2},y_{2})$
and
$C(x_{3},y_{3})$
are the vertices of
$ΔABC$
, find the coordinates of the centroid of the triangle.
Class 10
Math
All topics
Coordinate Geometry
Using the distance formula, show that the given points are collinear.
$(1,−1),(5,2)$
and
$(9,5)$
.
Class 10
Math
All topics
Coordinate Geometry
If the points
$A(4,3)$
and
$B(x,5)$
lie on a circle with the centre
$O(2,3)$
, find the value of x.
1
2
3
4
5
6
7
8
9
10
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page
1 / 2
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2
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