CAN YOU PLEASE HELP, I AM STUCK..THANKS
FIND THE DISTANCE BETWEEN (-3,2) AND (1,4)
FIND THE DISTANCE BETWEEN (-4,0) AND -5,-3)
DETERMINE WHETHER THE ROOT OF 77 IS RATIONAL OR IRRATIONAL.
THANKS IN ADVANCE, I APPRECIATE ALL OF THE HELP....
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Of course, I'll be happy to help you with your questions.
1. Finding the distance between (-3,2) and (1,4):
To find the distance between two points on a coordinate plane, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and states that the distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = √[(x2 - x1)² + (y2 - y1)²]
In this case, the points are (-3,2) and (1,4).
Plugging in the values into the formula:
d = √[(1 - (-3))² + (4 - 2)²]
d = √[(4)² + (2)²]
d = √[16 + 4]
d = √20
d ≈ 4.47
So, the distance between (-3,2) and (1,4) is approximately 4.47 units.
2. Finding the distance between (-4,0) and (-5,-3):
Using the same distance formula, we can find the distance between (-4,0) and (-5,-3).
Plugging in the values into the formula:
d = √[(-5 - (-4))² + (-3 - 0)²]
d = √[(-5 + 4)² + (-3)²]
d = √[(-1)² + 9]
d = √[1 + 9]
d = √10
d ≈ 3.16
So, the distance between (-4,0) and (-5,-3) is approximately 3.16 units.
3. Determining whether the square root of 77 is rational or irrational:
To determine if the square root of 77 is rational or irrational, we need to check if it can be written as a fraction (rational) or not (irrational).
The square root of 77 is an irrational number because it cannot be expressed as a fraction and its decimal representation goes on infinitely without repeating.
I hope this helps! Let me know if you have any more questions.