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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.
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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.?
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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.?.
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