What is the distance between points M(-3, 1)and N(7, -3)

Mathematics

1 answer:

Debora [2.8K]2 years ago

3 0

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!

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