coordinates, points and lines s1/w2/ho-1/g.11/math/rit-aya/2010-2011 name : _______________ class :...
TRANSCRIPT
COORDINATES, POINTS AND LINES
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
Name : _______________
Class : 10 ___Day/date :
_______________
point
Point can be determined location, but do not have the size (magnitude) / dimensionless
example:
. A .
Ppoint A point P
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
Line is set of the points that only have the length / one dimensional
From two points make a line
example
k
line k
A
B ray AB
BA line segment AB
Line
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
Y 4 B 3
2
1
X -3 -2 -1 0 1 2 3
A -1 -2
Fig. 1 S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
coordinates
points&lines
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
The distance between the points (x1, y1) and (x2,y2) (or the length of the line segment joining them) is
The distance between two points
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
Example:1. find the length of AB
B
x A
Fig. 2
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
answer:
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
2. Given A(-3,k) and B(9,-1), if the length of AB is 13 units, find possible values of k.
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
answer:
3. Given a triangle ABC, which A(-1,2), B(2,2) and C(2,6). find the length of each side of the triangle. Determine whether ∆ABC is a right-angled triangle, an isosceles triangle or neither of the above.
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
answer:
The mid-point of the line segment joining(x1, y1) and (x2,y2) has coordinates
The mid-point of a line segment
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
Example:
1. From Fig. 2, find the mid-point of A
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answer:
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
2. If M(-2,1) is the midpoint of AB, where A is (-3,2), find the coordinates of B.
answer:
3. A(1,5) and B(7,-9) are two points. AB divided into four equal parts at C, D and E. Find coordinates of C, D and E.
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
answer:
The gradient of the line joining (x1, y1) to (x2,y2) is
The gradient of a line segment
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
ExampleThe ends of a line segment are (a-b,a+b) and (a+b,a-b). Find the length of the line segment, its gradient and the coordinates of its mid point.
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
answer:
The equation of a line
• The equation of the line through
(x1,y1) with gradient m is;
y–y1=m(x-x1)
• The equation of the line through
A(x1,y1) and B(x2,y2) is;12
1
12
1
xx
xx
yy
yy
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
Example
1. Find the equation of the line through the point (2,-3) with gradient -1
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2. Find the equation of the line joining the points (3,4) and (-1,2)
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
answer:
The point of intersection of two lines
Suppose that you have two lines with equation 2x – y = 4 and 3x + 2y = -1. How do you find the coordinates of the point of intersection of these lines?
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
Parallel and Perpendicular Lines
• Parallel lines (//) Parallel lines have equal gradient m1=m2
• Perpendicular Lines ( ) Two lines with gradients m1 and m2 are perpendicular if; m1m2=-1
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
Example
1. A(2,1), B(3,4), C(-1,2) and D(-2,-1) are four points. a) which of the lines AB, BC, CD and DA are parallel? b) what type of quadrilateral is ABCD?
S1/W2/HO-1/G.11/Math/RIT-AYA/2010-2011
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2. A line is drawn through the point (-1,2) parallel to the line y + 5x = 2. Find its equation and that of the perpendicular line through the same point
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answer: