COORDINATE GEOMETRY Week commencing Monday 2nd November 2009

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Presentation transcript:

COORDINATE GEOMETRY Week commencing Monday 2nd November 2009 Learning Intention: Given a point and the gradient to be able to find the equation of a line. Contents: 1. Equation of a Straight Line from gradient and a point 2. Examples 3. Assignment 2 1

EQUATION OF A LINE FROM POINT & GRADIENT COORDINATE GEOMETRY EQUATION OF A LINE FROM POINT & GRADIENT If given the gradient of a line and a point, (x1, y1), on the line we can find the equation of line using the formula: y – y1 = m(x – x1) 2

EQUATION OF A LINE FROM POINT & GRADIENT COORDINATE GEOMETRY EQUATION OF A LINE FROM POINT & GRADIENT Example: Find the equation of the line with gradient 4 that passes through the point (1, 3). Solution: m = 4 (x1, y1) = (1, 3) Substituting into formula we get: y – 3 = 4(x – 1) y – 3 = 4x – 4 expanding brackets y = 4x – 4 + 3 simplifying y = 4x – 1 in form y = mx + c 3

EQUATION OF A LINE FROM POINT & GRADIENT COORDINATE GEOMETRY EQUATION OF A LINE FROM POINT & GRADIENT Example: Find the equation of the line with gradient -½ that passes through the point (5, 3). Solution: m = -½ (x1, y1) = (5, 3) Substituting into the formula we get: 4

EQUATION OF A LINE FROM POINT & GRADIENT COORDINATE GEOMETRY EQUATION OF A LINE FROM POINT & GRADIENT Example: The line y = 4x – 8 meets the x-axis at the point A. Find the equation of the line with gradient 3 that passes through the point A. Solution: We first need a point on the required line. We can get this by finding the coordinates of A. Let y = 0 to find where y = 4x – 8 meets the x –axis. 4x – 8 = 0 4x = 8 x = 2 coordinates of A are (2, 0) m = 3 (2, 0) Substitute into formula y – 0 = 3(x – 2) y = 3x - 6 5

COORDINATE GEOMETRY Assignment 2 Follow the link for Assignment 2 in the Moodle Course Area underneath Coordinate Geometry. This is a Yacapaca Activity. Assignments to be completed by 5:00pm on Monday 9th November 2009 6