Podcast
Questions and Answers
What is the distance between the points (0, 5) and (–5, 0)?
What is the distance between the points (0, 5) and (–5, 0)?
What is the length of the diagonal of the rectangle with vertices A (0, 3), O (0, 0) and B (5, 0)?
What is the length of the diagonal of the rectangle with vertices A (0, 3), O (0, 0) and B (5, 0)?
What is the perimeter of the triangle with vertices (0, 4), (0, 0) and (3, 0)?
What is the perimeter of the triangle with vertices (0, 4), (0, 0) and (3, 0)?
What is the area of the triangle with vertices A (3, 0), B (7, 0) and C (8, 4)?
What is the area of the triangle with vertices A (3, 0), B (7, 0) and C (8, 4)?
Signup and view all the answers
The coordinates of point P that divides the line segment joining points A (x1, y1) and B (x2, y2) in the ratio m1:m2 can be expressed as which of the following?
The coordinates of point P that divides the line segment joining points A (x1, y1) and B (x2, y2) in the ratio m1:m2 can be expressed as which of the following?
Signup and view all the answers
What is the distance between the points (2, 3) and (4, 7)?
What is the distance between the points (2, 3) and (4, 7)?
Signup and view all the answers
If the coordinates of point P are (1, 2) and point Q are (3, 4), what is the midpoint of the segment joining P and Q?
If the coordinates of point P are (1, 2) and point Q are (3, 4), what is the midpoint of the segment joining P and Q?
Signup and view all the answers
The area of a triangle with vertices at (1, 1), (4, 1), and (1, 5) is calculated using which formula?
The area of a triangle with vertices at (1, 1), (4, 1), and (1, 5) is calculated using which formula?
Signup and view all the answers
The coordinates of the point that divides the segment from A (2, 2) to B (4, 6) in the ratio 1:3 are:
The coordinates of the point that divides the segment from A (2, 2) to B (4, 6) in the ratio 1:3 are:
Signup and view all the answers
What is the perimeter of the triangle formed by the points (2, 1), (2, 4), and (5, 1)?
What is the perimeter of the triangle formed by the points (2, 1), (2, 4), and (5, 1)?
Signup and view all the answers
Study Notes
Distance between Points
- The distance between two points P (x1, y1) and Q (x2, y2) is calculated as : √((x2 - x1)^2 + (y2 - y1)^2)
- The distance between two points is the length of the line segment connecting them
Distance from Origin
- The distance of a point P (x, y) from the origin (0, 0) is calculated as √(x^2 + y^2)
Internal Division Point
- The coordinates of a point P that divides the line segment joining points A (x1, y1) and B (x2, y2) internally in the ratio m1:m2 are calculated as: ((m1 * x2 + m2 * x1) / (m1 + m2), (m1 * y2 + m2 * y1) / (m1 + m2))
Mid-point of Line Segment
- The coordinates of the mid-point of the line segment joining points P (x1, y1) and Q (x2, y2) are calculated as: ((x1 + x2)/2, (y1 + y2)/2)
Distance Between Specific Points
- The distance between the points (0, 5) and (-5, 0) is 5√2
Rectangle Properties
- AOBC, with vertices A (0, 3), O (0, 0), and B (5, 0), is a rectangle.
- The length of its diagonal is calculated using the Pythagorean theorem: √(AB)^2 + (OB)^2 = √5^2 + 3^2 = √34
Triangle Properties
- The perimeter of a triangle with vertices (0, 4), (0, 0), and (3, 0) is the sum of all its sides: 4 + 3 + √(3^2 + 4^2) = 12
- The area of a triangle with vertices A (3, 0), B (7, 0), and C (8, 4) is calculated using the formula: (1/2) * base * height = (1/2) * 4 * 4 = 8
Distance Between Two Points
- The distance between P ( x1 , y1 ) and Q ( x2 , y2 ) is ( ) ( )2 2 2 1 2 1– –x x y y+
- The distance of a point P (x,y) from the origin is 2 2 x y+
Section Formula
- The coordinates of the point P which divides the line segment joining the points A ( x1 , y1 ) and B ( x2 , y2 ) internally in the ratio m1 : m2 are 1 2 2 1 1 2 2 1 1 2 1 2 + + , + + m x m x m y m y m m m m
Mid-point Formula
- The coordinates of the mid-point of the line segment joining the points P (x1, y1) and Q (x2, y2) are ( 1 2 2 1+ x x , 1 2 2 1+ y y )
Example 1
- The distance between the points (0, 5) and (–5, 0) is (B) 5 2
Example 2
- AOBC is a rectangle with vertices A (0, 3), O (0, 0), and B (5, 0).
- The length of its diagonal is (C) 34.
Example 3
- The perimeter of a triangle with vertices (0, 4), (0, 0), and (3, 0) is (C) 11
Example 4
- The area of a triangle with vertices A (3, 0), B (7, 0), and C (8, 4) is (A) 14
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers the fundamental concepts of distance between points, including calculations for distances from the origin, internal division points, and midpoints of line segments. Additionally, it explores properties of rectangles and the length of diagonals. Perfect for students studying geometry.
