Find the point equidistant from the three points (-6,,1) and (0,0).

The point equidistant from the three points (-6,0),(-3,1) and (0,0) is (-3,-3)

Solution:

The given three points are A (-6, 0), B (–3, 1) and C (0, 0)

Let P (x, y) be the point equidistant from these three points.

Distance between two points is given as  

Where are the x and y co-ordinates

The distance between A (-6, 0) and P(x, y) is:

Using the distance formulae,

On taking square root we get,

--- eqn 1

The distance between B(-3, 1) and P(x, y) is:

On taking square root we get

--- eqn 2

The distance between C(x, y) and P (0, 0) is:

-- eqn 3

By equating equation 1 = equation 2 to find the value of  y

In both the expression is common so we can cancel it.

On expanding we get,

12x = -36

x = -3.

Now find the value of y using equation 3.

Hence the required points are (-3,-3).

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.