Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Given the vector v has an initial point at (8,8) and a terminal point at (8,2), find the exact value of ||v||. Answer:

Given the vector v \mathbf{v} has an initial point at (8,8) (8,8) and a terminal point at (8,2) (8,2) , find the exact value of ∥v∥ \|\mathbf{v}\| .\newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Transformations of absolute value functions: translations and reflectionsright chevron icon

Full solution

Q. Given the vector v \mathbf{v} has an initial point at (8,8) (8,8) and a terminal point at (8,2) (8,2) , find the exact value of ∥v∥ \|\mathbf{v}\| .\newlineAnswer:
  1. Calculate Differences and Square: To find the magnitude of vector vv, we need to calculate the difference in the xx-coordinates and the yy-coordinates between the terminal point and the initial point. The magnitude of vector vv, denoted as ∣∣v∣∣||v||, is given by the formula:\newline∣∣v∣∣=((x2−x1)2+(y2−y1)2)||v|| = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}\newlinewhere (x1,y1)(x_1, y_1) is the initial point and (x2,y2)(x_2, y_2) is the terminal point.
  2. Substitute Given Points: Substitute the given points into the formula. The initial point is (8,8)(8,8) and the terminal point is (8,2)(8,2). Therefore, x1=8x_1 = 8, y1=8y_1 = 8, x2=8x_2 = 8, and y2=2y_2 = 2.\newline∣∣v∣∣=((8−8)2+(2−8)2)||v|| = \sqrt{((8 - 8)^2 + (2 - 8)^2)}
  3. Simplify Squares and Sum: Calculate the differences and square them.\newline∣∣v∣∣=(0)2+(−6)2||v|| = \sqrt{(0)^2 + (-6)^2}
  4. Calculate Square Root: Simplify the squares and sum them up.\newline∣∣v∣∣=0+36||v|| = \sqrt{0 + 36}
  5. Calculate Square Root: Simplify the squares and sum them up.\newline∣∣v∣∣=(0+36)||v|| = \sqrt{(0 + 36)}Calculate the square root to find the magnitude.\newline∣∣v∣∣=36||v|| = \sqrt{36}\newline∣∣v∣∣=6||v|| = 6

More problems from Transformations of absolute value functions: translations and reflections

Question
Find g(x) g(x) , where g(x) g(x) is the translation 2 2 units left of f(x)=∣x∣ f(x) = |x| .\newlineWrite your answer in the form a∣x−h∣+k a|x - h| + k , where a a , h h , and k k are integers.\newlineg(x)= g(x) = ______\newline
Get tutor helpright-arrow

Posted 5 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the reflection across the y y -axis of f(x)=∣x∣ f(x) = |x| .\newlineWrite your answer in the form a∣x−h∣+k a|x - h| + k , where a a , h h , and k k are integers.\newlineg(x)= g(x) = ______\newline
Get tutor helpright-arrow

Posted 8 months ago

Question
The graph of y=∣x∣ y=|x| is reflected across the x x -axis and then scaled vertically by a factor of 77 .\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=7∣x∣ y=7|x| \newline(B) y=−7∣x∣ y=-7|x| \newlineC) y=17∣x∣ y=\frac{1}{7}|x| \newline(D) y=−17∣x∣ y=-\frac{1}{7}|x|
Get tutor helpright-arrow

Posted 8 months ago

Question
The graph of y=∣x∣ y=|x| is scaled vertically by a factor of 66 .\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=∣x−6∣ y=|x-6| \newline(B) y=6∣x∣ y=6|x| \newline(C) y=16∣x∣ y=\frac{1}{6}|x| \newline(D) y=∣x−16∣ y=\left|x-\frac{1}{6}\right|
Get tutor helpright-arrow

Posted 7 months ago

Question
The graph of y=∣x∣ y=|x| is scaled vertically by a factor of 13 \frac{1}{3} .\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=∣x∣−3 y=|x|-3 \newline(B) y=−3∣x∣ y=-3|x| \newline(C) y=13∣x∣ y=\frac{1}{3}|x| \newline(D) y=∣x∣−13 y=|x|-\frac{1}{3}
Get tutor helpright-arrow

Posted 8 months ago

Question
The graph of y=∣x∣ y=|x| is shifted to the left by 66 units.\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=∣x+6∣−6 y=|x+6|-6 \newline(B) y=∣x−6∣−6 y=|x-6|-6 \newline(C) y=∣x∣−6 y=|x|-6 \newline(D) y=∣x+6∣ y=|x+6|
Get tutor helpright-arrow

Posted 7 months ago

Question
The graph of y=∣x∣ y=|x| is reflected across the x x -axis and then scaled vertically by a factor of 14 \frac{1}{4} .\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=−4∣x∣ y=-4|x| \newline(B) y=∣x∣−4 y=|x|-4 \newline(C) y=−14∣x∣ y=-\frac{1}{4}|x| \newline(D) y=∣x−4∣ y=|x-4|
Get tutor helpright-arrow

Posted 8 months ago

Question
The graph of y=∣x∣ y=|x| is shifted down by 99 units.\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=∣x∣−9 y=|x|-9 \newline(B) y=∣x+9∣ y=|x+9| \newline(C) y=∣x∣+9 y=|x|+9 \newline(D) y=∣x−9∣ y=|x-9|
Get tutor helpright-arrow

Posted 10 months ago

Question
y=13x+5y=2x \begin{array}{l} y=\frac{1}{3} x+5 \\ y=2 x \end{array} \newlineConsider the given system of equations. If (x,y) (x, y) is the solution to the system, then what is the value of y+x y+x ?
Get tutor helpright-arrow

Posted 3 months ago

Question
13x+3y=4 \frac{1}{3} x+3 y=4 \newline2x−4=2y 2 x-4=2 y \newlineConsider the given system of equations. If (x,y) (x, y) is the solution to the system, then what is the value of x−y x-y ?
Get tutor helpright-arrow

Posted 2 months ago

View all (49)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant