Question

ind the values of y for which the distance between tite points A(3,-1) and B(11, y) is 10 units.​

Answer 1

Here, as per the provided question we have to find the value of y for which the distance between the points A(3,-1) and B(11,y) is 10 units –

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CORRECT QUESTION :

Find the values of y for which the distance between the points A(3,-1) and B(11,y) is 10 units.

GIVEN :

• The value provided for finding the distance is A(3,-1) and B(11,y) is 10 units.

TO FIND :

• The value of y, when the information of distance is provided = ?

STEP -BY-STEP EXPLAINATION :

Now, as per the provided information we will find the value of y when A(3,-1) and B(11,y) is 10 units.

$⟹ \sqrt{(3 - 11)^{2} } + ( -1 - 4) ^{2} = 10$

[ Now, here substituting the values ]

$⟹ \sqrt{( { - 8})^{2} } + {( { - 1})^{2}} - 2 \: ( - 1) \: ( - y) + {y}^{2} = 10$

$⟹ \: \sqrt{64 + 1 - 2y + {y}^{2} } = 10$

Now, here we have got √64+1-2y+y² = 10. So, we will remove your the sign of square root :

$⟹ \: {y}^{2} - 2y + 65 = 100$

$⟹ \: {y}^{2} - 2y - 35 = 0$

$⟹ \: {y}^{2} - 7y + 5y - 35 = 0$

$⟹ \: y \: (4 - 7) + 5(4 - 7) = 0$

$⟹ \: (y - 7) \: (y + 5) = 0$

Here, there are the two conditions of bringing the answer (value) as per the provided question –

(y-7) and (y+5) that is considered as –

ㅤㅤㅤㅤㅤ y = 7 and y = -5

Therefore, both can be written here y = 7 is also an appropriate answer for this question and

y = -5 is also considered as an appropriate answer for this question.

So, Now the value of y for which is the distance between the points A(3,-1) and B(11,y) is 10 units = y = 7 or y = -5.

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