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The diagram below, NOT drawn to scale, models the above situation in a Cartesian plane. $\triangle{ABD}$ has vertices $A(1;4), B(-3;1)$ and $D(5;-2)$. The angle formed by the x-axis and $AE$ is $\alpha$ and the angle formed by the x-axis and $AD$ is $\beta$ 1. The length of AD (leave answer in simplified surd form)
2. The coordinates of $M$, the midpoint of $AD$
3. The equation of straight line $MC$ (in the form $ax+by+c=0$) if $MC \parallel AB$
4. The size of $\alpha$
5. The size of $B\hat{A}D$
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## 1 Answer

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1. AD = √[(5-1)^2 + (-2-4)^2]

= √52

= 2√13

2. M = ( 1+5)/2 ; ( 4-2)/2

= (3;1)

3. grad AB = 1-4/-3-1

= 3/4

grad MC = 3/4, since its parallel to AB

y-1 = 3/4 (x-3)

3x-4y-5 = 0

4. tanx = 3/4  (alpha)

= 36.87 degrees

5. grad AD = -2-4/5-1 = -3/2

tanB = -3/2

B = 123.69 degrees

BAD = 123.69- 36.87, ext < of triangle

= 86.82 degrees

by Diamond (42,470 points)

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