Question

estion 10. Find the value of a, if the distance between the two points: (4,-5),(-2, a) is V85 units.​

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11th

Maths

Straight Lines

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If the distance between the...

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If the distance between the points (5,−2), (1,a) is 5 units, find the value of a.

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ANSWER

⇒ The distance between two points P(x

1

,y

1

) and Q(x

2

,y

2

) is given by

PQ=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

here P(x

1

,y

2

)=P(5,−2)

& Q(x

2

,y

2

)=Q(1,a)

& PQ=5 units

i.e. 5=

(1−5)

2

+(a−(−2))

2

Taking square on both side we get,

∴25=(−4)

2

+(a+2)

2

∴25−16=(a+2)

2

∴(a+2)

2

=9

∴a

2

+4a+4=9

∴a

2

+4a−5=0

∴a

22

+5a−a−5=0

∴a(a+5)−1(a+5)=0

∴a(a+5)−1(a+5)=0

∴a−1=0 or a+5=0

a=1 or a=−5

→ The values of a will be 1 or −5