Breezing through Coordinate Geometry Mathematics 0580 Online Classes

Breezing through Coordinate Geometry Mathematics 0580 Online Classes @ Sciency

Overview Ø Introduction to Speaker and Sciency. Ø Syllabus topics and what it expects us to cover. Ø What is MEANT by Geometry, Coordinates, and the terms combined. Ø The importance Lines, gradients, and line equation. Ø Calculating gradients, lengths, midpoints. Ø Parallel lines and perpendicular lines. Ø Combined Formula list. Ø Walking through past – paper questions. Ø Doubts – q/a

Compiled Formulas

Few basic concepts • • • Geometry - the math of shape, size, position of figures, and dimension of things. Measurements with lines, points etc. Coordinates OR co – ordinates – pin points the location of some place, thing etc. Used in maps. Coordinate Geometry: Where the position of a point is defined using coordinates. It tells us about the relative position of two points on the graph. A point is represented by (x, y) For example, if you wanted to go 3 units up and 3 units for the right, it will be (3, 3). 5 units up and 3 units to the left will take you to (-3, 5) and so on. The first number represented in the brackets is the x – value and the number after the comma is the y – value of that point. Try locating (5, -5).

Lines Represents a relationship between two points. y = ? , where ? is a formula in terms of x. y = 2 x – 2 Every value of x you put in the formula it will give you a value of y back, since the formula is doing work to give a value of y back – we will call it a function. So y = 2 x – 2 is a function. • We can plot this function a graph. • • x – value -3 -2 -1 0 1 2 3 y - value -8 -6 -4 -2 0 2 4 • We can in fact do this for any formula and plot it on a graph. • TIP: Make sure you substitute the x value properly and get the y – value correctly. -3 to 3 is an ideal range.

Intercepts: * • y – intercept: at which point does the graph intersect the y – axis (represented by “c”) • x – intercept: at which point does the graph intersect them x - axis x – intercept The EASIEST WAY to find intercepts: • If you notice, when the graph cuts the y – axis, the x value is 0. Therefore if you simply put x as 0 in y = 2 x -2 you will get the value of c. y - intercept • Same goes for the x – intercept. The value at which the graph cuts the x – axis, the y – value is 0. So if you put y as 0 in the equation, you will get the value of x.

Gradient is the rate of change of something. For example, acceleration is a gradient – it measures the rate of change of velocity. Represented by In Coordinate Geometry, gradient is how quickly the y value changes over the x value on the line. Straight Line Equation: y = mx + c m – gradient c – y - intercept Q] Find the gradient between points (0, -2) and (2, 2) Gradient = [2 – (-2)] / [2 – 0] = [4 / 2] = 2

Straight line equation y = mx + c gradient y - intercept How to find the straight line equation of a line passing through known co – ordinates – 1) Find the gradient of the line using the formula and substituting x 1, y 1, x 2, and y 2. 2) Substitute values from one coordinate and the gradient. 3) Rearrange the formula to find the value of c. 4) Lastly, just put the values of m and c.

Length and Mid-point • We can find out the length between two points anywhere on the graph. Example, let’s find the length between the points (6, 4) and (-5, 3). • (6, 4) = (x 1, y 1) so x 1 = 6 and y 1 = 4 • (-5, 3) = (x 2, y 2) so x 2 = -5 and y 2 is 3 • Once substituted, you will get the length as 11. 02. cm.

Perpendicular and Parallel Lines • Parallel lines are lines on the graph that will never meet no matter how long you will continue the lines for. • Parallel lines have equal gradients. M 1 = M 2 Perpendicular lines meet each other at 90 degrees. Perpendicular lines have gradients that are negative reciprocals of each other M 1 x M 2 = -1

Walkthrough Questions!

Doubts? Ask away!