Maths Coordinate Geometry Flashcards
(25 cards)
What is the definition of coordinate geometry?
Coordinate geometry is the study of geometry using a coordinate system.
What are the two axes in a Cartesian coordinate system?
The two axes are the x-axis (horizontal) and the y-axis (vertical).
What is the point of intersection of the x-axis and y-axis called?
The point of intersection is called the origin.
What are the coordinates of the origin?
(0, 0)
In a coordinate plane, what does the first quadrant represent?
The first quadrant represents points where both x and y coordinates are positive.
True or False: The coordinates of a point are written in the form (x, y).
True
Fill in the blank: The distance formula in coordinate geometry is used to find the distance between two points and is given by _____.
d = √[(x2 - x1)² + (y2 - y1)²]
What is the formula to find the midpoint of a line segment joining two points (x1, y1) and (x2, y2)?
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
What are the coordinates of the point A if A is located at (3, -4)?
The coordinates of point A are (3, -4).
What is the slope of a line passing through the points (2, 3) and (5, 11)?
The slope is (11 - 3) / (5 - 2) = 8 / 3.
True or False: The x-coordinate is always written first in an ordered pair.
True
What is the formula to calculate the area of a triangle formed by three points in the coordinate plane?
Area = 1/2 | x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) |
What does it mean if two lines are parallel in coordinate geometry?
Two lines are parallel if they have the same slope.
What is the equation of a line in slope-intercept form?
The equation is y = mx + b, where m is the slope and b is the y-intercept.
What is the y-intercept of the line given by the equation y = 2x + 3?
The y-intercept is 3.
Fill in the blank: A point on the x-axis has a y-coordinate of _____.
0
What is the significance of the slope in a linear equation?
The slope indicates the steepness and direction of the line.
True or False: The coordinates of a point in the third quadrant are both negative.
True
What does the term ‘collinear points’ refer to?
Collinear points are points that lie on the same straight line.
If point B is at (4, 5) and point C is at (4, -2), what is the distance between points B and C?
The distance is |5 - (-2)| = 7.
What is the equation of a vertical line passing through the point (3, 2)?
The equation is x = 3.
What is the equation of a horizontal line passing through the point (4, -1)?
The equation is y = -1.
What do you call the horizontal distance between two points in the coordinate plane?
The horizontal distance is called the difference in x-coordinates.
What do you call the vertical distance between two points in the coordinate plane?
The vertical distance is called the difference in y-coordinates.
