What is the distance between points (4,0) and (-2,-3)

Hi! I'm happy to help!

To solve this equation, we need to find how much distance is between the y coordinates, how much distance is between the x coordinates, and then use the Pythagorean Theorem.

Let's start with finding the distance between the x coordinates. The first x coordinate is 4, and the second is -2. This means that the distance in x is 6.

Next, we need to find how much distance is between the y coordinates. The first y point is at the y coordinate 0, and the second is at the y coordinate -3. This means that the distance in y is 3.

Now we use the Pythagorean Theorem, which says that a²+b²=c²

A and b refer legs of a right triangle, and c refers to the hypotenuse (longest side) of the right triangle. Imagine the two points on a line, the direct distance is the c, and the y and x movements alone are a and b.

Let's say x is a, and y is b. Let's insert our values:

6²+3²=c²

36+9=c²

45=c²

To find c, we need to find the square root of 45

√45

6.708203...

Rounds to about 6.7 in tenths.

So, the distance between those two points is about 6.7.

I hope this was helpful, keep learning! :D

1) c 2143.6 cm

2) c 113.0 m

3) a 33.5 ft

4)   d 2 cm

5) c 20 mm

6) 180 in

7) d 120 ft

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square