Question

2.
1) find the value of 4 if the distance between
points AC2,-2) and B (-1, 4) is 5
AB2= [(-1)-2] + [y-(-2)] 2
52 = (-3)2 +__2
25 = ____
16 = (y+2)
Y+2= ____
y+2 = 14
y= 4-2 or y= 4-2
y=__ or y=__
Value of y is ___​

Answer 1

Appropriate Question :- Find the value of k if distance between points A (2,-2) and B (-1, k) is 5.

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Given :- The distance between points A(2,-2) and B(-1, k) is 5.

⠀

To find :- The value of k?

Solution :-

The given points are A(2, - 2) and B(-1, y).

Here,

• x₁, = 2
• y₁ = -2
• x₂ = -1
• y₂ = k.

We know that,

• AB = √{(x₂ - x₁)² + (y₂ - y₁)²}.

Putting all values in formula, we get:

→ 5 = √{(-1 - 2)² + (k - (-2))²}

→ (5)² = (-3)² + (k - (-2))²

→ 25 = (-3)² + (k + 2)²

→ 25 = 9 + (k + 2)²

→ 25 - (k + 2)² = 9

→ -(k + 2)² = 9 - 25

→ -(k + 2)² = -16

→ (k + 2)² = 16

→ k + 2 = √16

→ k + 2 = 4

→ k = 4 - 2

→ k = 2 (Ans.)

Hence, the required value of k is 2.

Answer 2

Answer:

Correct Question :-

• Find the value of k if the distance between two points is A(2 , - 2) and B(- 1 , k) is 5.

Given :-

• Distance between two points A(2 , - 2) and B(- 1 , k) is 5.

To Find :-

• What is the value of k.

Formula Used :-

$\clubsuit$ Distance Formula :

$\longmapsto \sf\boxed{\bold{\pink{Distance =\: \sqrt{{(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2}}}}}$

Solution :-

$\mapsto$ A(2 , - 2)

$\mapsto$ B(- 1 , k)

Let,

• x₂ = - 1
• x₁ = 2
• y₂ = k
• y₁ = - 2

According to the question by using the formula we get,

$\implies \sf 5 =\: \sqrt{{(- 1 - 2)}^{2} + {(k - (- 2))}^{2}}$

$\implies \sf 5 =\: \sqrt{{(- 3)}^{2} + {(k + 2)}^{2}}$

$\implies \sf 5 =\: \sqrt{9 + {(k + 2)}^{2}}$

$\implies \sf {(5)}^{2} =\: 9 + {(k + 2)}^{2}$

$\implies \sf 5 \times 5 =\: 9 + {(k + 2)}^{2}$

$\implies \sf 25 =\: 9 + {(k + 2)}^{2}$

$\implies \sf 25 - 9 =\: {(k + 2)}^{2}$

$\implies \sf 16 =\: {(k + 2)}^{2}$

$\implies \sf \sqrt{16} =\: (k + 2)$

$\implies \sf 4 =\: (k + 2)$

$\implies \sf 4 =\: k + 2$

$\implies \sf 4 - 2 =\: k$

$\implies \sf 2 =\: k$

$\implies \sf\bold{\red{k =\: 2}}$

$\therefore$ The value of k is 2 .