Question

Find all possible values of y for which the distance between the points A(2,-3) and B(10, y) is 10 units.
please elaborate step by step​

Answer 1

___________________✔️

Question:

Find all possible values of y for which the distance between the points A(2, – 3) and B(10, y) is 10 units.

Answer:

Given, the distance AB = 10 units

By distance formula, as shown below:

AB = √{(10 – 2)2 + (y – (– 3))2}

10 = √{(8)2 + (y + 3)2}

10 = √{64 + y2 + 6y + 9}

10 = √{73 + y2 + 6y}

Squaring both sides we get

100 = 73 + y2 + 6y

On solving the equation, 100 = 73 + y2 + 6y

On solving the equation, 100 = 73 + y2 + 6y⇒ 27 + y2 + 6y = 0

⇒ y2 + 6y + 27 = 0

⇒(y – 3)(y + 9) = 0

⇒ y = 3 or y = – 9

∴ The values of y can be 3 or – 9

${} \huge \mathfrak \red{hope \: it \: helps \: you..}$

Answer 2

Answer:

The all possible valuse of y is :--

y = 3 or y = -9