Question

find the value of 'a' when the distance between the points (3,a) and (4,1) is
$\sqrt{10}$




who is answering first I will mark sa brainleast
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Answer 1

Step-by-step explanation:

line AB

Distance AB=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

⇒

10

=

(1−a)

2

+(4−3)

2

Squaring both sides, we get

⇒10=(1−a)

2

+(4−3)

2

⇒10=1+a

2

−2a+1=0

⇒a

2

−2a−8=0

⇒a

2

−4a+2a−8=0

⇒a(a−4)+2(a−4)=0

⇒(a−4)(a+2)=0

∴a=−2 or a=4

Answer 2

Let d be distance and (3,a) be (x1,y2) and (4,1) be (x2,y2).

x1=3. x2=4

x1=3. x2=4y1=a. y2=1

x1=3. x2=4y1=a. y2=1d=√10. ...(Given)

$d = (y2 - y1) \div (x2 - x1)$

√10 = (1-a) ÷ (4-3)

√10 = (1-a) ÷ (4-3)√10 = (1-a) ÷ 1

√10 = (1-a) ÷ (4-3)√10 = (1-a) ÷ 1√10 = 1-a

√10 = (1-a) ÷ (4-3)√10 = (1-a) ÷ 1√10 = 1-aa=1-√10