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Coordinate geometry is one of the most fundamental and essential chapters in Class 10 mathematics. With its diverse applications and the scope for solving a variety of problems, it has become an important topic for students aiming to score high in their exams. At Educart, we’ll explore everything you need to know about learning coordinate geometry in Important Questions of Coordinate Geometry Class 10, extra practice techniques, and strategies with the help of available resources like solution PDFs.
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Soln.
(c) both i) and ii)
Explanation:
Section Formula:
The section formula can be used to find the coordinates of a point that divides a line segment internally in a given ratio.
Thus, the section formula can be used to find A's coordinates.
Distance Formula:
The distance formula can be used to calculate the distance between two points.
Thus, the distance formula can also be used to find A's coordinates.
Soln.
Preeti's final position
Distance traveled east for 12 minutes: = Speed × Time
= 30×1/5
=6 km.
(6,0)
Distance traveled south for 3 minutes: = Speed × Time
= 60×1/20
=3 km.
(3,0)
Since she is driving south, this means she moves 3 km along the negative y-axis. So, her final position is: (6,−3)
Arun's final position
Distance traveled west for 4 minutes: = Speed × Time
= 30×1/15
=2 km.
(-2,0)
Distance traveled north for 4 minutes: = Speed × Time
= 45×1/20
=2 km.
(2,0)
Since he is driving north, this means he moves 3 km along the positive y-axis. So, his final position is: (−2,3)
d= √(x2−x1)2+(y2−y1)2
d= √(-2-6))2+(3- (-3))2
d= √(-8)2+(6)2
d= √64+36
d= √100
d= 10km
The straight-line distance between Preeti's office and Arun's office is 10 km.
Soln.
The center of the circle is O(2,−5)
A(1,2) and B(x,y) are the endpoints of the chord ABABAB.
M(5,−2) is the midpoint of AB where the perpendicular from the center O touches the chord.
M= x1+x2 / 2, y1+y2 / 2
(5,-2)= 1+x / 2, 2+y / 2
1+x / 2 = 5
x=9
2+y / 2 = -2
y=−6
B(9,−6)
Soln.
RT=3⋅TG.
T(x,y)= ((mx2+nx1)/m+n, (my2+ny1)m+n)
x= 3(10)+1(−6)/3+1
x= 30−6/4
x= 24/4
x= 6
y= 3(11)+1(−5)/3+1
y= 33−5/4
y= 28/4
y= 7
The coordinates of the treasure are:
T(6,7)
Soln.
i) Find the coordinates of hole B.
BC=2×BA
B divides AC in the ratio 1:2 (from A to C)
B(x,y)= ((mx2+nx1)/m+n, (my2+ny1)m+n)
B(x,y)= (1(9)+2(−6)/1+2, 1(−4)+2(−1)/1+2)
B(−1,−2)
ii) Find the shortest distance covered by the ball.
d=√(x2−x1)2+(y2−y1)2
d=√(-1−2)2+((-2)−3)2
d=√(-3)2+(-5)2
d=√9+25
d=√34
Soln.
The vertices of the rhombus are given as:
Key Properties of a Rhombus:
a) Find the coordinates of the point where both the diagonals PR and QS intersect.
M= (x1+x2)/2 , (y1+y2)/2 ,
M= (2+(-2))/2 , (-3+1)/2 ,
M= 0/2 , (-2)/2 ,
M= 0 , -1
Thus, the diagonals intersect at the point (0,−1)
b) Find the coordinates of the fourth vertex S.
M(0,−1) is the midpoint,
Q(6,5) and S(x,y) are the endpoints.
(6+x)/2, (5+y)/2=(0,−1)
For x:
(6+x)/2 = 0
6+x=0
x=−6
For y
(5+y)/2= -1
5+y=−2
y=−7
Thus, the coordinates of S are (−6,−7)
Soln.
(i) What are the coordinates of points P and Q?
The given line is:
x+2y=2
For the x-axis
Substitute y=0 into x+2y=2
x+2(0)=2⟹x=2
So, Q has coordinates (2,0)
For the y-axis
Substitute x=0 nto x+2y=2
0+2y=2⟹y=1
So, P has coordinates (0,1)
Thus, the coordinates of P and Q are:
P(0,1)and Q(2,0)
(ii) What is the area of the triangle formed? Show your steps.
O(0,0)
P(0,1),
Q(2,0)
area of a △ = ½ ∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣
area of a △ = ½ ∣0(1-0)+0(0−0)+02(0−1)∣
area of a △ = ½ ∣0+0+2(−1)∣
area of a △ = ½ ∣0+0-2∣
area of a △ = ½ ∣-2∣
area of a △ = ½ 2
area of a △ = 1
Soln. (b) Isosceles right-angled triangle
Explanation:
AB=√(x2−x1)2+(y2−y1)2
AB= √(1−5)2+(4-1)2
AB= √(4)2+(3)2
AB= √16+9
AB= √25
AB= 5
BC =√(x2−x1)2+(y2−y1)2
BC = √(8−1)2+(5-4)2
BC = √(7)2+(1)2
BC = √49+1
BC = √50
BC = 5√2
CA =√(x2−x1)2+(y2−y1)2
CA = √(8−5)2+(5-1)2
CA = √(3)2+(4)2
CA = √9+16
CA = √25
CA = 5
Two sides are equal: AB=CA=5
This makes the triangle isosceles.
Checking for a right angle:
BC2=AB2+CA2
(5√2)2=52+52
(50)=25 + 25
(50)=50
The condition holds true, so the triangle is right-angled.
The triangle △ABC is an isosceles right-angled triangle.
Soln.
The equation of a circle with center at the origin (0,0) and radius r is:
x2+y2=r2
x2+y2=(½)2
x2+y2=(1/4)
x=−y
y=y
(−y)2+y2=¼
(y)2+y2=¼
2y2=¼
y2=¼ / 2
y2= 8
y= ± √2/4
(−y,y)= (−√2/4, √2/4)
(−y,y)= -(−(√2/4), -√2/4)
(−y,y)= (√2/4, -√2/4)
points on the circle of radius 1/2 that are of the form (−y,y) are:(−√2/4, √2/4) or (√2/4, -√2/4)
Coordinate geometry, often referred to as analytic geometry, is the study of geometry using a coordinate system. In Class 10, this topic deals majorly with the Cartesian plane, where students learn how to solve problems related to points, lines, distances, and areas using coordinates (x, y) on a two-dimensional plane.
The core concepts include:
As exams draw near, the important questions from Coordinate Geometry class 10 play a significant role in your preparation. We carefully curate these questions to cover the wide variety of concepts and problem-solving approaches you might encounter in your exams. Practicing these can not only build confidence but also provide insights into the kinds of questions that frequently appear in board exams.
Class 10 is an important and tough year for students. The marks obtained in board exams are a reflection of your hard work and consistency. One of the best ways to ensure success is by practicing important questions in Coordinate Geometry Class 10. But what makes these questions so important?
Effectively utilizing coordinate geometry in class 10 important questions is a crucial aspect of exam preparation. This detailed guide will help you maximize these resources:
To truly excel in the coordinate geometry chapter of Class 10, here are some unique tips:
Coordinate geometry class: 10 important questions play a major role in improving your understanding of this chapter and preparing you for the board exams. By practicing a diverse set of class 10 coordinate geometry extra questions, using available solutions PDFs, and following the tips, you’ll be well on your way to learning coordinate geometry and scoring high in your exams.
To top the exam, the key is consistent practice, understanding core concepts, and using resources like solution PDFs wisely. Make a study plan, stick to it, and don’t forget to review your mistakes.
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