College Entrance Test Review Math Session 4 Coordinate Geometry Formulas for the Slope of a line, Midpoint, Distance between any two points, Equations of a Line
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Cartesian Coordinate System X-axis Y-axis Point – described as an ORDERED PAIR
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Recall: Undefined terms in geometry? POINT – now described as (x, y) LINE – we will define as an equation: where x & y are unknowns, and a and b are known quantities. PLANE – the Cartesian plane (previous slide)
Given the points P(7, 2) and Q(3,-5) in a plane. Find the midpoint of these two points.
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Midpoint – is like getting the AVERAGE – is a POINT, so your answer must have two coordinates. – Get the average of the X coordinates, and the average of the Y coordinates Midpoint Formula:
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Given the points P(7, 2) and Q(3,-5) in a plane. Find the midpoint of these two points.
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Distance between Two Points (or the length of a line segment) Given the points P(7, 2) and Q(3,-5) in a plane. Find the distance between these two points.
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How do we get the length of the hypotenuse of a right triangle? Pythagorean Theorem:
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