Answer:
Answer rounded to nearest tenth:
[tex] \rm \: Distance \boxed { \approx 48.20}[/tex]
Distance between the two points in exact form:
[tex] \boxed{\rm \: Distance = \sqrt{2326.19}} [/tex]
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:
[tex] \rm \: Distance = \sqrt{( x_{2} - x_{1}) {}^{2} +(y_{2} -y_{1} ) {}^{2} } [/tex]
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:
[tex] \rm \: Distance = \sqrt{(15.3 - 59.5) {}^{2} + (14.9 - 34.2) {}^{2} } [/tex]
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:
[tex] \rm \: Distance = \sqrt{ ( - 44) {}^{2} + ( - 19.3) {}^{2} }[/tex]
Solve for exponents:
[tex] \rm \: Distance = \sqrt{1953.64 + 372.49} [/tex]
Add the integers inside the radical:
[tex] \boxed{\rm \: Distance = \sqrt{2326.19}} [/tex]
It could be rewritten as:
[tex] \rm \: Distance \boxed{≈48.20}[/tex]
Hence,the distance between two points is
- [tex] \boxed{\rm \: Distance = \sqrt{2326.19}} [/tex]
OR
- [tex] \rm \: Distance \boxed{≈48.20}[/tex]
Actual answer would be 48.2 rounded to nearest tenth,as per the question.
