Question

Let us calculate and see that for what value of y, the distance of the two points (2, y) and (10, –9) will be 10.
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Answer 1

Answer:

y = -3, -15

Step-by-step explanation:

Given that,

There are two points in coordinate plane,

• P = (2,y)
• Q = (10,-9)

Also, the distance between them is 10 units.

To find the valye of y.

We know that,

Distance between two points (a,b) and (c,d) is given by,

• $\sqrt{ {(c - a)}^{2} + {(d - b)}^{2} }$

Therefore, we will get,

$= > \sqrt{ {(10 - 2)}^{2} + {(y + 9)}^{2} } = 10 \\ \\ = > {8}^{2} + {(y + 9)}^{2} = {(10)}^{2} \\ \\ = > {(y + 9)}^{2} + 64 = 100 \\ \\ = > {(y + 9)}^{2} = 100 - 64 \\ \\ = > {(y + 9)}^{2} = 36 \\ \\ = > {(y + 9)}^{2} = {( \pm6)}^{2} \\ \\ = > y + 9 = \pm6 \\ \\ = > y = \pm6 - 9 \\ \\ = > y = -3 \: \: and \: \: - 15$

Hence, required values of y are -3 and -15.

Answer 2

Step-by-step explanation:

Answer:

y = -3, -15

Step-by-step explanation:

Given that,

There are two points in coordinate plane,

P = (2,y)Q = (10,-9)

Also, the distance between them is 10 units.

To find the valye of y.

We know that,

Distance between two points (a,b) and (c,d) is given by,

Therefore, we will get

Hence, required values of y are -3 and -15.