Point m is located at (4,6) on a coordinate grid. point m is translated 8 units to thr left and 9 units down to create point m'. which measurement is closest to the distance between point m and point m' in units?

Well, i would use the distance formula to find the distance between the two points. Only issue- you do not have the other point, so lets find it!

We have the point 4,6. 4 is the x, and 6 is the y.

Lets start with 4 since the x works with the left and right aspect of the location. It says M has been translated 8 units to the left, meaning we go back 8. So if we are at 4, and we go back (A.K.A. Subtract) 8, we will be at -4.

Now lets move onto the y, which works with the up and down aspect of the location. It says M has been translated 9 unites down, meaning the point will be heading down and getting smaller. So if we are at 6, and we go down (A.K.A. subtract) 9, then we will be at -3.

So now we have the coordinates of point M (4,6) and point M' (-4,-3) so we can now complete the distance formula!

The distance formula helps determine the distance between two points. It looks like this: D = √(x₂-x₁)²+(y₂-y₁)²

Though it does not matter which order you use the coordinates in, i am choosing to use M and then M'.

So, starting with the X, X₂ will be -4 and X₁ will be 4.
Again, starting with the Y, Y₂ will be -3 and Y₁ will be 6.

So, the formula plugged in will look like this: d = √(-4 - 4)² + (-3 - 6)²

Solving it out, we first need to work within the parenthesis. Can you solve it?

Our outcome will be this: -8² + -9². But, since we are squaring (And a negative times a negative equals a positive) you can just write 8² + 9²

8²= 64
9²= 81

64+81 = 145.

So, the distance between point M and point M' would be 145 units

Hope this helps!

If it does not, please let me know so i can try to help!