show that the points (0,-2), (2,4) and (-1,-5) are collinear.
Answers
A ( 0 , -2 ) and B ( 2 , 4 )
Here,
X1 = 0 , Y1 = -2 and X2 = 2 , Y2 = 4.
Therefore,
AB = ✓(X2 - X1 )² + ( Y2 - Y1 )²
AB = ✓( 2 - 0 )² + ( 4 + 2 )²
AB = ✓4 + 36
AB = √40 = ✓2 × 2 × 2 × 5
AB = 2√10 units.
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B ( 2 , 4 ) and C ( -1 , - 5 )
Here,
X1 = 2 , Y1 = 4 and X2 = -1 , Y2 = -5.
Therefore,
BC = ✓( X2 - X1 )² + ( Y2 - Y1)²
BC = ✓ ( -1 - 2 )² + ( -5 - 4 )²
BC = ✓9 + 81
BC = ✓90 = ✓2 × 3 × 3 × 5
BC = 3√10 units.
_______________________________
A ( 0 , -2 ) and C ( -1 , - 5 )
Here,
X1 = 0 , Y1 = -2 and X2 = -1 , Y2 = -5
AC = ✓ ( X2 - X1 )² + ( Y2 - Y1 )²
AC = ✓ ( -1 - 0)² + ( -5 + 2 )²
AC = ✓1 + 9
AC = √10 units.
_________________________________
AB + AC = 2√10 + √10 = 3√10 units.
And,
BC = 3√10 units.
Thus,
AB + AC = BC.
Hence,
The given points A , B , C are collinear.
Answer:
Step-by-step explanation:
Let A(0,-2) , B ( 2 , 4 ) and C ( -1 , -5 ) be the given points.
A ( 0 , -2 ) and B ( 2 , 4 )
Here,
X1 = 0 , Y1 = -2 and X2 = 2 , Y2 = 4.
Therefore,
AB = ✓(X2 - X1 )² + ( Y2 - Y1 )²
AB = ✓( 2 - 0 )² + ( 4 + 2 )²
AB = ✓4 + 36
AB = √40 = ✓2 × 2 × 2 × 5
AB = 2√10 units.
________________________________
B ( 2 , 4 ) and C ( -1 , - 5 )
Here,
X1 = 2 , Y1 = 4 and X2 = -1 , Y2 = -5.
Therefore,
BC = ✓( X2 - X1 )² + ( Y2 - Y1)²
BC = ✓ ( -1 - 2 )² + ( -5 - 4 )²
BC = ✓9 + 81
BC = ✓90 = ✓2 × 3 × 3 × 5
BC = 3√10 units.
_______________________________
A ( 0 , -2 ) and C ( -1 , - 5 )
Here,
X1 = 0 , Y1 = -2 and X2 = -1 , Y2 = -5
AC = ✓ ( X2 - X1 )² + ( Y2 - Y1 )²
AC = ✓ ( -1 - 0)² + ( -5 + 2 )²
AC = ✓1 + 9
AC = √10 units.
_________________________________
AB + AC = 2√10 + √10 = 3√10 units.
And,
BC = 3√10 units.
Thus,
AB + AC = BC.
Hence,
The given points A , B , C are collinear.