1)
Gradient (m) of the line =Tan45
=1
Let x= abscissa
ΔxΔY= gradient
x−(2−5)6−(−29)=1
6+29=x+25
⟹x=8
2)
Gradient of the line =2−213−7−0=4.57
The angle that the line makes with horizontal
=Tan−1(4.57)
=57.26
Angle that the line makes with any vertical line
=90−57.26=32.74
3)
Angle between the lines
=Tan−1(32)=33.69
Angle between L1 and horizontal
=Tan−1(−1)=−45°
Angle between L2 and horizontal
=−45+ -33.69
=−78.69
Slope of L2=Tan(−78.69)
=−5
Or between L2 and horizontal =−45+33.69
=−11.31
Slope of L2= Tan(−11.31)
=−0.2
4) Angle between L2andL1=Tan−1(21)
=26.565
Angle between L2 and horizontal
=45+26.565=71.565Slope=tan(71.565)
=3
5) side a=∣∣1−77−4∣∣
(−6)2+32=√45
Side b =∣∣7−−34−−4∣∣
=102+82)=√164
Side c=∣∣1−−37−−4∣∣
=42+112=√137
Using cosine rule
45=164+137−2164×137cosθ
Cosθ=299.8256
θ=31.36
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