Question

What is the distance between the points (59.5, 34.2) and (15.3, 14.9)? Enter your answer rounded to the nearest tenth (0.1).

Answer 1

Answer rounded to nearest tenth:

`\rm \: Distance \boxed { \approx 48.20}`

Distance between the two points in exact form:

`\boxed{\rm \: Distance = √(2326.19)}`

Step by step explanation:

Given two points:

• (59.5, 34.2) and (15.3, 14.9)

To Find:

• The distance between the two points

Solution:

Recall the formulae that is used to find Distance from two points:

`\rm \: Distance = \sqrt{( x_(2) - x_(1)) {}^(2) +(y_(2) -y_(1) ) {}^(2) }`

According to the Question, on the formula,

• (x_2 , x_1) = (15.3,59.5)
• (y_2 , y_1) = (14.9,34.2)

So substitute them on the formula of distance:

`\rm \: Distance = \sqrt{(15.3 - 59.5) {}^(2) + (14.9 - 34.2) {}^(2) }`

Simplify now using PEMDAS:

• P = parentheses
• E = exponents
• M = multiplication
• D = Division
• A = Addition
• S = subtraction

First subtract the integers inside the parentheses which is inside the radical:

`\rm \: Distance = \sqrt{ ( - 44) {}^(2) + ( - 19.3) {}^(2) }`

Solve for exponents:

`\rm \: Distance = √(1953.64 + 372.49)`

Add the integers inside the radical:

`\boxed{\rm \: Distance = √(2326.19)}`

It could be rewritten as:

`\rm \: Distance \boxed{≈48.20}`

Hence,the distance between two points is

• 
  `\boxed{\rm \: Distance = √(2326.19)}`

OR

• 
  `\rm \: Distance \boxed{≈48.20}`

Actual answer would be 48.2 rounded to nearest tenth,as per the question.

Answer 2

48.2

Explanation:

√(x2-x1)²+(y2-y1)²

√(15.3-59.5)² +(14.9-34.2)²

√(-44.2)² + (-19.3)²

√1953.64+372.49

√2326.13

48.2