Discuss the keywords in question Has the same gradient as…

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Presentation transcript:

Discuss the keywords in question Has the same gradient as…

Perpendicular and Parallel Lines Know what the terms parallel and perpendicular mean (especially in relation to straight lines). Know what a perpendicular bisector is. Understand the connection between the gradients for lines that are parallel and lines that are perpendicular. Be able to explain how to find the equations of lines that are perpendicular to another line or pair of points. Also be able to find the equation of the perpendicular bisector of two points.

Parallel lines Parallel lines have the same gradient m If asked for a parallel line to y = mx + c going through the point (x 1, y 1 ) you treat this like one point & with gradient. Sub. m and x 1 & y 1 into

Example Find the line parallel to y = 2x + 5, that passes through (2,7)

Parallel lines

a) b)

Perpendicular Lines Perp. Lines do not have the same gradient They have a negative reciprocal. What? This just means this:

Perp. Lines When asked to find a line perp. to another and going through the point (x 1, y 1 ) Find m 2 first. TIP: Change sign, and flip it.

Perp. Lines Once you have found m 2,then use line equation. Sub. m and x 1 & y 1 into

Example Find the line perp. to y = 2x + 5, that passes through (2,7)

a) b)

Try a k question A line that is perpendicular to the line that connects A(5,7) and B(7,-9) passes through the point (6,-1) and (-2, k) find the value of k k=-2

Right angles You might be asked to prove two lines crossing form a right angle between them (a.k.a that they are perp. To each other) The proof is simple:

Right angles The points A,B and C are (2,5); (5,9) and (6,2) respectively. Find the gradient of AB Find the gradient of AC and hence state whether the angle  BAC is 90 o

Try one out A(6,4); B(9,8); C(10,0) Find the gradients of AB; AC and BC Decide if ABC is a right-angled triangle. Gradients AB  4 / 3 AC  1 BC  8 None of the gradients are negative reciprocals to each other so it is not a right-angled triangle.

Independent Study Exercise 1F p23 (solutions p416)