QQuestionMathematics
QuestionMathematics
# What is the distance between point A and point B?
My Progress
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:: Identify the coordinates of point A and point B.
The coordinates of point A are ($$3, 2$$) and the coordinates of point B are ($$7, 6$$).
Step 2:: Calculate the difference between the x-coordinates of point A and point B.
x_{B} - x_{A} = 7 - 3 = 4
Step 3:: Calculate the difference between the y-coordinates of point A and point B.
y_{B} - y_{A} = 6 - 2 = 4
Step 4:: Calculate the distance between point A and point B using the distance formula.
d(A, B) = \sqrt{4^2 + 4^2}
The distance formula is derived from the Pythagorean theorem and is given by: Substitute the values calculated in steps 2 and 3 into the distance formula:
Step 5:: Simplify the expression inside the square root.
d(A, B) = \sqrt{32}
So,
Step 6:: Simplify the square root.
\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}
Final Answer
The distance between point A and point B is 4\sqrt{2} units.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students