Question

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Answer 1

Value of y is - 15

Step-by-step explanation:

Value of y is - 15

Let the points be A (2,y) and B (10,-9) represent the line with distance between them as 10 Units.

We know that the Distance between two points is equal  to $\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$

Here, $x_{2} = 10 \ and\ y_{2}$= -9

Also, $x_{1} = 2 \ and \ y_{1}$ = y

Applying the above Distance formula we get -  

⇒ $\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$ = 10

⇒ $\sqrt{(10 - 2)^{2} + (-9 - y)^{2}}$ = 10

⇒ $\sqrt{(8)^{2} + (-9 - y)^{2}}$= 10

⇒ $\sqrt{64 + (-9 - y)^{2}}$ = 10

Squaring both sides we get -

64 + (-9 - y)^{2} = 100

⇒ (-9 - y)^{2} = 100 - 64

⇒ (-9 - y)^{2} = 36

or (-9 - y) = 6

or - y = 6 + 9

⇒ y = - 15

So, Value of y is - 15