Class 10 Exam > Class 10 Questions > The length of a line segment is of 10 units a...
Start Learning for Free
The length of a line segment is of
10
units and the coordinates of one-end-point are
(2, -3) If the abscissa of the other end is
10, find the ordinate of the other end.?
10
units and the coordinates of one-end-point are
(2, -3) If the abscissa of the other end is
10, find the ordinate of the other end.?
Most Upvoted Answer
The length of a line segment is of 10 units and the coordinates of one...
Given Information:
- Length of line segment = 10 units
- Coordinates of one end-point = (2, -3)
- Abscissa of the other end = 10
Explanation:
To find the ordinate of the other end of the line segment, we first need to understand the concept of distance formula and coordinate geometry.
Distance Formula:
The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by the formula:
\[ \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \]
Calculations:
Given that the length of the line segment is 10 units, and the coordinates of one end-point are (2, -3). Let the coordinates of the other end-point be (10, y).
Using the distance formula:
\[ \sqrt{(10 - 2)^2 + (y - (-3))^2} = 10 \]
Solving this equation, we get:
\[ \sqrt{8^2 + (y + 3)^2} = 10 \]
\[ 8^2 + (y + 3)^2 = 100 \]
\[ 64 + y^2 + 6y + 9 = 100 \]
\[ y^2 + 6y - 27 = 0 \]
Now, solve this quadratic equation to find the value of y.
Hence, the ordinate of the other end of the line segment is the solution to the above quadratic equation.
- Length of line segment = 10 units
- Coordinates of one end-point = (2, -3)
- Abscissa of the other end = 10
Explanation:
To find the ordinate of the other end of the line segment, we first need to understand the concept of distance formula and coordinate geometry.
Distance Formula:
The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by the formula:
\[ \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \]
Calculations:
Given that the length of the line segment is 10 units, and the coordinates of one end-point are (2, -3). Let the coordinates of the other end-point be (10, y).
Using the distance formula:
\[ \sqrt{(10 - 2)^2 + (y - (-3))^2} = 10 \]
Solving this equation, we get:
\[ \sqrt{8^2 + (y + 3)^2} = 10 \]
\[ 8^2 + (y + 3)^2 = 100 \]
\[ 64 + y^2 + 6y + 9 = 100 \]
\[ y^2 + 6y - 27 = 0 \]
Now, solve this quadratic equation to find the value of y.
Hence, the ordinate of the other end of the line segment is the solution to the above quadratic equation.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
The length of a line segment is of 10 units and the coordinates of one-end-point are(2, -3) If the abscissa of the other end is 10, find the ordinate of the other end.?
Question Description
The length of a line segment is of 10 units and the coordinates of one-end-point are(2, -3) If the abscissa of the other end is 10, find the ordinate of the other end.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The length of a line segment is of 10 units and the coordinates of one-end-point are(2, -3) If the abscissa of the other end is 10, find the ordinate of the other end.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of a line segment is of 10 units and the coordinates of one-end-point are(2, -3) If the abscissa of the other end is 10, find the ordinate of the other end.?.
The length of a line segment is of 10 units and the coordinates of one-end-point are(2, -3) If the abscissa of the other end is 10, find the ordinate of the other end.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The length of a line segment is of 10 units and the coordinates of one-end-point are(2, -3) If the abscissa of the other end is 10, find the ordinate of the other end.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of a line segment is of 10 units and the coordinates of one-end-point are(2, -3) If the abscissa of the other end is 10, find the ordinate of the other end.?.
Solutions for The length of a line segment is of 10 units and the coordinates of one-end-point are(2, -3) If the abscissa of the other end is 10, find the ordinate of the other end.? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of The length of a line segment is of 10 units and the coordinates of one-end-point are(2, -3) If the abscissa of the other end is 10, find the ordinate of the other end.? defined & explained in the simplest way possible. Besides giving the explanation of
The length of a line segment is of 10 units and the coordinates of one-end-point are(2, -3) If the abscissa of the other end is 10, find the ordinate of the other end.?, a detailed solution for The length of a line segment is of 10 units and the coordinates of one-end-point are(2, -3) If the abscissa of the other end is 10, find the ordinate of the other end.? has been provided alongside types of The length of a line segment is of 10 units and the coordinates of one-end-point are(2, -3) If the abscissa of the other end is 10, find the ordinate of the other end.? theory, EduRev gives you an
ample number of questions to practice The length of a line segment is of 10 units and the coordinates of one-end-point are(2, -3) If the abscissa of the other end is 10, find the ordinate of the other end.? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup