Question

Find x if distance between points L(x,7) and M(1,15) is 10

Answer 1

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Answer 2

Answer:

x = -5, 7

Step-by-step explanation:

In the question,

We know that the distance between two points is given by,

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

Now,

The points are L(x, 7) and M(1, 15).

Now also the distance between the points is given,

Distance = 10

So,

$10 = \sqrt{(15-7)^{2}+ (1-x)^{2}} \\On\ squaring\ both\ sides, we\ get,\\100=64+(1-x)^{2}\\36=(1-x)^{2}\\So,\\1-x=-6,6\\So,\\when,\\1-x=-6\\x=7\\when,\\1-x=6\\x=-5$

Therefore, the value of x is given by, x = -5 and 7.

Therefore, there are two possible values of x for which the distance between the points is 10.