How do you find a possible value for a if the points (4,a), (8,4) has a distance of d=2√5?

1 Answer
Nityananda
Apr 27, 2017

a = 6 or 2

Explanation:

We know the distance between two points = √(x2−x1)2+(y2−y1)2 where (x1,y1)=(4,a)and(x2,y2)=(8,4)

Hence √(8−4)2+(4−a)=2√5 [as per question]

or, (8−4)2+(4−a)2=[2√5]2 [ squiring both sides]

⇒42+16−8a+a2=20

⇒a2−8a+16+16−20=0

⇒a2−8a+12=0

⇒a2−2a−6a+12=0

⇒a(a−2)−6(a−2)=0

⇒(a−6)(a−2)=0

⇒(a−6)=0,(a−2)=0

⇒a=6or2

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