Answer:
d = 2√29 units
Step-by-step explanation:
M(-3, 1)and N(7, -3)
To find the distance between these two points, we want to use the distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Plug in the values.
d = √[(7 - (-3))² + (-3 - 1)²]
Simplify the parentheses.
d = √[(7 + 3)² + (-4)²]
d = √[(10)² + (-4)²]
Simplify the exponents
d = √[(100 + 16)]
Simplify the parentheses by adding.
d = √[116]
Simplify the brackets with the square root.
- Since 116 is not a perfect square, we need to find two numbers that multiply to 116. One number must be a perfect square. The other must be a prime number.
- 4 • 29 = 116. Therefore √4 • √29 = √116
- √4 = 2. Therefore 2√29 = √116
d = 2√29 units
Hope this helps!
