Question
find a parametric vector equation for the segment joining:The midpoint of the segment with endpoints $\mathbf{Q}(-5,2)$ and $\mathbf{R}(1,6)$ and the point one-third of the way from $\mathbf{S}(-2,6)$ to $\mathbf{T}(1,9)$.
Step 1
The formula for the midpoint \(\mathbf{M}\) of a segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ \mathbf{M} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Substituting the coordinates of \(\mathbf{Q}\) and \(\mathbf{R}\): Show more…
Show all steps
Your feedback will help us improve your experience
Khushbu Rani and 62 other educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find a vector equation and parametric equations for the line segment that joins $P$ to $Q$. $$P(-2,1,0), \quad Q(5,2,-3)$$
Vector Functions
Vector Functions and Space Curves
$13-16=$ Find a vector equation and parametric equations for the line segment that joins $P$ to $Q .$ $$P(2,0,0), \quad Q(6,2,-2)$$
VECTORS AND THE GEOMETRY OF SPACE
(a) Suppose that the line segment from the point $P\left(x_{0}, y_{0}\right)$ to $Q\left(x_{1}, y_{1}\right)$ is represented parametrically by $x=x_{0}+\left(x_{1}-x_{0}\right) t$ $y=y_{0}+\left(y_{1}-y_{0}\right) t$ $(0 \leq t \leq 1)$ and that $R(x, y)$ is the point on the line segment corresponding to a specified value of $t$ (see the accompanying figure). Show that $t=r / q,$ where $r$ is the distance from $P$ to $R$ and $q$ is the distance from $P$ to $Q$ (b) What value of $t$ produces the midpoint between points $P$ and $Q ?$ (c) What value of $t$ produces the point that is three-fourths of the way from $P$ to $Q$ ? (GRAPH CAN'T COPY)
Functions
Parametric Equations
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD