Answer:
<em>Answer rounded to nearest tenth:</em>
![\rm \: Distance \boxed { \approx 48.20}](https://tex.z-dn.net/?f=%20%5Crm%20%5C%3A%20Distance%20%5Cboxed%20%7B%20%5Capprox%2048.20%7D)
<em>Distance between the two points in exact form:</em>
![\boxed{\rm \: Distance = \sqrt{2326.19}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%5Crm%20%5C%3A%20Distance%20%3D%20%20%5Csqrt%7B2326.19%7D%7D%20)
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} }](https://tex.z-dn.net/?f=%20%5Crm%20%5C%3A%20Distance%20%3D%20%20%5Csqrt%7B%28%20x_%7B2%7D%20-%20x_%7B1%7D%29%20%7B%7D%5E%7B2%7D%20%20%20%2B%28y_%7B2%7D%20%20-y_%7B1%7D%20%29%20%7B%7D%5E%7B2%7D%20%7D%20)
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} }](https://tex.z-dn.net/?f=%20%5Crm%20%5C%3A%20Distance%20%3D%20%20%5Csqrt%7B%2815.3%20-%2059.5%29%20%7B%7D%5E%7B2%7D%20%20%2B%20%2814.9%20-%2034.2%29%20%7B%7D%5E%7B2%7D%20%7D%20)
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} }](https://tex.z-dn.net/?f=%20%5Crm%20%5C%3A%20Distance%20%3D%20%5Csqrt%7B%20%20%28%20-%2044%29%20%7B%7D%5E%7B2%7D%20%20%2B%20%28%20-%2019.3%29%20%7B%7D%5E%7B2%7D%20%20%20%7D)
Solve for exponents:
![\rm \: Distance = \sqrt{1953.64 + 372.49}](https://tex.z-dn.net/?f=%20%5Crm%20%5C%3A%20Distance%20%3D%20%20%5Csqrt%7B1953.64%20%2B%20372.49%7D%20)
Add the integers inside the radical:
![\boxed{\rm \: Distance = \sqrt{2326.19}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%5Crm%20%5C%3A%20Distance%20%3D%20%20%5Csqrt%7B2326.19%7D%7D%20)
It could be rewritten as:
![\rm \: Distance \boxed{≈48.20}](https://tex.z-dn.net/?f=%20%5Crm%20%5C%3A%20Distance%20%5Cboxed%7B%E2%89%8848.20%7D)
Hence,the distance between two points is
OR
Actual answer would be 48.2 rounded to nearest tenth,as per the question.