Find the distance between the following two points: (-4,10) and (-10, -1). Round to the nearest TENTH.

1 answer:

6 0

Answer:

distance = 12.5

Step-by-step explanation:

Use the distance formula to find the distance between any two points

√[(x₂ - x₁)² + (y₂ - y₁)²]

Points: (-4, 10) and (-10, -1)

Step 1. Plug these points into the formula (where the first point indicates the firsts x and y coordinates and the second point indicates the seconds x and y coordinates)

√[(-10 - (-4))² + (-1 - 10)²]

Step 2. Subtract

√[6² + (-11)²]

Step 3. Simplify (exponents)

√[36 + 121]

Step 4. Add

√157

Step 5. Simplify (radical)

12.52

Step 6. Round to the nearest tenth

12.5

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The short leg of a 90-45-45 triangle is 3 and the long leg is 7. What is the hypotenuse?

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The short leg of a 90-45-45 triangle is 3 and the long leg is 7. The hypotenuse would be $c = \sqrt{58}$ .

<h3>What is the Pythagoras theorem?</h3>

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

The short leg of a 90-45-45 triangle is 3 and the long leg is 7.

Since this is a right triangle, we can use the Pythagoras theorem

a^2+b^2 = c^2

where a and b are the legs and c is the hypotenuse

$3^2 + 7^2 = c^2\\\\9 + 49 = c^2\\\\58 = c^2\\\\c = \sqrt{58}$