To reflect a shape in the line y = −x using coordinate geometry To reflect a shape in the line y = x using coordinate geometry, the x-coordinate becomes the y-coordinate and the y-coordinate becomes the x-coordinate. To reflect a shape in the y-axis using coordinate geometry, the y-coordinate stays the same, but the x-coordinate changes sign (becomes negative if it is positive and vice versa). To reflect a shape in the x-axis using coordinate geometry, the x-coordinate stays the same, but the y-coordinate changes sign (becomes negative if it is positive and vice versa). To translate a shape using coordinate geometry, change the x-coordinate of each point by how far you move the shape horizontally and change the y-coordinate of each point by how far you move the shape vertically.Ī reflection is a flip of a shape about a line (called the line of reflection).
Read more about how to convert polar to Cartesian coordinates Read more about how to convert Cartesian to polar coordinates
Read more about how to read off a point from polar coordinates Read more about how to draw a point from polar coordinates Polar coordinates can be converted to Cartesian coordinates.
To read off a point from polar coordinates, measure how far across the point is from the pole to find the radial coordinate and find what angle the point is (in the counter-clockwise direction) from the polar axis to find the angular coordinate.Ĭartesian coordinates can be converted to polar coordinates. To draw a point from polar coordinates, use the radial coordinate to measure how far the point is from the pole and use the angular coordinate to find what angle the point is (in the counter-clockwise direction) from the polar axis. It tells you what angle the point is (in the counter-clockwise direction) from the polar axis. The angular coordinate is the second number in the pair of numbers used to describe polar coordinates. It tells you how far a point is from the pole. The radial coordinate is the first number in the pair of numbers used to describe polar coordinates. Polar coordinates work by measuring how far the point is from a reference point (called the pole) and what angle it is from a reference direction (called the polar axis). Polar coordinates are used to describe the position of a point on a graph. Read more about how to read off a point from Cartesian coordinates Read more about how to draw a point from Cartesian coordinates To read off a point from Cartesian coordinates, measure how far across the x-axis the point is to find the x-coordinate and measure how up (or down) the y-axis the point is to find the y-coordinate. Read Off a Point from Cartesian Coordinates To draw a point from Cartesian coordinates, use the x-coordinate to measure how far across the x-axis the point is and use the y-coordinate to measure how up (or down) the y-axis the point is. It tells you how far up (or down) the vertical y-axis a point is on a graph. The y-coordinate is the second number in the pair of numbers used to describe Cartesian coordinates. It tells you how far across the horizontal x-axis a point is on a graph. The x-coordinate is the first number in the pair of numbers used to describe Cartesian coordinates. Click the MORE button to learn more.Ĭartesian coordinates are used to describe the position of a point on a graph. The lessons are grouped into mini-curriculum to help you organise your learning.Ī brief description is given for each mini-curriculum. Coordinate geometry allows us to do this. We might want be interested in how a shape is moved. We might be interested in the distance between two points. Here are some examples from coordinate geometry. The coordinates can be used to describe points on lines, curves and shapes. The x-coordinate is on the left, the y-coordinate is on the right. The x-coordinate (x) and the y-coordinate (y) are then written in brackets, separated by a comma. In general, if the point is y units up the y-axis, its y-coordinate is y.Įach point can be written as a pair of coordinates: The y-coordinate measures how far up the point is (in the vertical direction) up the y-axis. In general, if the point is x units along the x-axis, its x-coordinate is x. The x-coordinate measures how far across the point is (in the horizontal direction) along the x-axis.
The Merriam-Webster dictionary defines a graph as "a diagram (such as a series of one or more points, lines, line segments, curves, or areas)."Ĭoordinates are used to describe the position of a point on the graph.