1) A(4, –4)

B(2, 4)

C(1, 3)

D (–1, k)

Find the value of k which makes line segment AB:

a) perpendicular to line segment CD

b) parallel to line segment CD

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2) While drawing the plans for a highway project, a surveyor needs to find
the equation for a line that represents the path the high-tension wires will follow.
The line he needs will be parallel to 2x – 5y – 1500 = 0 and
include point P(500, 100). Write the equation of this line

a) in general form

b) in symmetric form.

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3) The diagram below depicts a map of a trapezoidal city lot. Find its area in km ².

.

Solutions

1) a) to make AB perpendicular to CD, we make slopes negative reciprocals.

Slope of AB = therefore slope of CD = ¼.

b) to make AB // CD, make slopes the same.

Slope of AB = – 4, so

.

2) The slope of 2x – 5y – 1500 = 0 is 2/5

a) so the equation of the line is:

or 2x – 5y – 500 = 0 in general form.

b) From 2x – 5y – 500 = 0 we get that a, the x-intercept is 250

and b, the y-intercept is –100

the equation of the line in symmetric form is:

3) Find the Area of ABCD

We need lengths of BC and AD and the height h, distance from B to AD.

So, we need the equation of AD in general form.

a) lengths of the bases:

b) equation of AD in General Form:

Slope of AD =

c) Find h the height of the trapezoid:

So the area of the trapezoid is ½ (b₁ + b₂ )h or

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