CO-ORDINATE GEOMETRY

Each of the following pairs of line segments are perpendicular (at right-angles to
each other). Work out the gradients of each pair of lines.
i) AB and AC. ii) DE and DF. iii) GH and GI.
iv) JK and JL. v) MN and MO. vi) PQ and PR.
14. a) Which of the following lines are parallel to the line with equation y = 2x + 1 ?
i) y = 2x 3 ii) y = 1 2x iii) y = 1 x + 1 2
iv) y = 5 + 2x.
b) Which of the following lines are perpendicular to the line with equation
y = 2x + 1?
i) y = 2x 3 ii) y = 1 2x iii) y = 1 x + 1 2
iv) y = 5 + 2x.
c) Which of the following lines are parallel to the line with equation y = 3x + 2 ?
i) y = 4x + 2 ii) y = 2 1 x 3 iii) y = 1 x + 1 3
iv) y = 3x 1.
d) Which of the following lines are perpendicular to the line with equation
y = 3x + 2 ?
i) y = 4x + 2 ii) y = 2 1 x 3 iii) y = 1 x + 1 3
iv) y = 3x 1.
e) Which of the following lines are parallel to the line with equation y = 2 4x ?
i) y = 4x + 1 ii) y = 3 4x iii) y = 1 x + 1 4
iv) y = 1 x 1. 4
f) Which of the following lines are perpendicular to the line with equation
y = 2 4x ?
i) y = 4x + 1 ii) y = 3 4x iii) y = 1 x + 1 4
iv) y = 1 x 1. 4
15. For each of the following, calculate the gradients of AB and CD and hence determine
whether the line AB is parallel or perpendicular to the line CD.
a) A(0, 1), B(1, 1), C(1, 5), D(1, 1)
b) A(1, 1), B(3, 2), C(1, 1), D(0, 1)
c) A(3, 3), B(3, 1), C(1, 1), D(1, 7)
d) A(2, 6), B(1, 9), C(2, 11), D(0, 1).
16. The points A(1, 5), B(4, 1) and C(2, 4) form a triangle ABC.
a) Calculate the gradients of AB, BC and AC.
b) Show that the angle ABC = 90 o .
{Hint: check the product of the gradients of AB and BC etc.}
c) Find the area of the triangle ABC.
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