Ch 8- Coordinate Geometry of Straight Lines

Distance between two points
√ (X2-X1)2 +(y2-y1)2
(distance formula)

given that slope of L1 will not equal to 0 and slope of L2 will also not equal to 0
if L1 perpendicular to L2 the slope of L1 times L2 =-1

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find the distance
A(6,3) and B((-2,3)

determine three point are collinear
A(-1,-3), B(1,-1), C(6,4)

it is given that the vertices of triangle ABC are A(7,5),B(-5,4) and C (-3,0) prove triangle ABC is a right angle

slope = y2-y1/x2-x1

the distance of AB√ (-2-6)2 +(3-3)2
=8

find the slope of AB
A(2,3) and B(4,3)

slope of AB
(3-3)/4-2
=0

slope of AB
-1+3/1+1=1

slope of BC
4+1/6-1=1

they are collinear

given that L1// L2
The slope of L1 =slope of L2
conversely
if slope of L1 = slope of L2
the slope of L1//L2

L1 passes through (-2,3) and (0,0)

slope of L1 =3-0/-2-0=-3/2

slope of L2= -3/2

slope of L1=slope of L2

L1//L2

slope of BC =0-4/-3+5
=-2

slope of AC 0-5/-3-7
=1/2

slope of BC times slope of AC
-2 times 1/2 =-1

BC perpendicular to AC
triangle ABC is a right angle.