Apps. and Interpretation for IBDP Maths Ebook 1 | Page 111

Exercise 31
1. The straight line L
1
passes through the points A( � 4, 6) and B( � 2, 0) .
(a) Find the gradient of L
1
.
[2]
(b) Find the equation of L
1
, giving the answer in general form.
[3]
C is a point on the x -axis such that OB � OC , where O is the origin. Another straight
line L
2
passes through the point C and is parallel to L
1
.
(c) Find the equation of L
2
, giving the answer in slope-intercept form.
D is the mid-point of AC .
[3]
(d) Find the coordinates of D .
Another straight line L
3
passes through the point D and is perpendicular to L
1
.
[2]
(e) Find the equation of L
3
, giving the answer in general form.
k
(f) It is given that CD � BD . Find the value of k .
5
[3]
[4]
10
2. The straight line L
1
passes through the points A(0, k ) and B(40, 30) . C(20, 25) is the
mid-point of AB .
(a) Find the value of k .
(b) Find the gradient of L
1
.
(c) Find the equation of L
1
, giving the answer in slope-intercept form.
Another straight line L
2
passes through the point A and is perpendicular to L
1
.
[2]
[2]
[2]
(d) Write down the equation of L
2
, giving the answer in slope-intercept form.
Another straight line L
3
passes through the point D( k , 0) and is perpendicular to L
1
.
[3]
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