Question

.2 Using Distance formula, check whether following points are collinear or not.
a.L (4, -1), M (1, -3), N(-2, -5)
b. A(-5, 4) B(-2, -2), C(3, -12)

Answer 1

Step-by-step explanation:

$distance = \sqrt{ {(x2 - x1)}^{2} } + {(y2 - y1}^{2}$

a. Let LN be line.

length of LN:

LN=√(-2-4)²+(-5+1)²

=√(-6)²+(-4)²

=√36+16=√52=2√13units.

LM=√(1-4)²+(-3+1)²

=(-3)²+(-2)²=√9+4=√13units.

MN =√(-2-1)²+-5+3)²

=√(-3)²+(-2)²=√9+4=√13units.

LN+MN=√13+√13=2√13=LN

Therefore, points L,M,N are collinear.

b. Let AC be line.

AC=√(3+5)²+(-12-4)²

=√(8)²+(-16)²=√64+256=√320=8√5units.

AB=√(-2+5)²+(-2-4)²

=√(3)²+(-6)²=√9+36=√45=3√5units.

BC=√{3+2)²+(-12+2)²

=√(5)²+(-10)²=√25+100=√125=5√5 units.

AB+BC=3√5+5√5=8√5units=AC.

Therefore, points A,B,C are colliner.

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Answer 2

Answer:

answer attached in photos