Hi, I'm happy to help!
To solve this, we need to find the distance in x coordinate values, y coordinate values, then use the Pythagorean Theorem to solve for the distance.
First, let's find the distance in x coordinate values. Our first x coordinate value is -6, and our second is 2. From here, we subtract.
-6-2=-8
Since we have a negative number, we use absolute value, which says how far the number is from 0.
I-8I
8
The distance in x coordinate values is 8.
Next, we find the distance in y coordinate values. our first y coordinate is -5, and our second is 0, now, let's subtract.
-5-0=-5
I-5I
5
The distance in y coordinate values is 5.
From here, we use the Pythagorean Theorem, which states that a²+b²=c².
This has to do with right triangles. Think about drawing a line down to the y coordinate of the other point, then to the x coordinate. Now, drawing a line straight from point to point. Now, you have a right triangle, and we are trying to find c, the direct distance of the line going from point to point. Let's say that our x distance is a, and our y distance is b.
Let's plug in the values:
8²+5²=c²
64+25=c²
89=c²
To find c, we need to find the square root of 89.
√89=c
9.433981132...=c
Since this number goes on forever, we need to round.
Rounding to the nearest thousandth:
9.434
Nearest hundredth:
9.43
Nearest tenth:
9.4
Depending on what the question asks, use one of these values.
To conclude, The distance between the two points is about 9.43 units.
I hope this was helpful, keep learning! :)