Solve Lesson 33 Page 81 Math 10 SBT – Kite>

Topic

Which of the following equations is a parametric equation for a line parallel to the line .?

x – 2y + 3 = 0?

A. $$\left\{ \begin{array}{l}x = – 1 + 2t\\y = 1 + t\end{array} \right.$$ B. $$\left\{ \begin{ array}{l}x = 1 + 2t\\y = – 1 + t\end{array} \right.$$ C. $$\left\{ \begin{array}{l}x = 1 + t\ \y = – 1 – 2t\end{array} \right.$$ D. $$\left\{ \begin{array}{l}x = 1 – 2t\\y = – 1 + t\end{array} \right.$$

Solution method – See details

Step 1: Find the lines whose VTCP multiplies the scalar times the VTPT of the line x – 2y + 3 = 0 equals 0

Step 2: Get a point on the lines found in step 1, replace that point’s coordinates into the line PT

x – 2y + 3 = 0. If that point is not on the line x – 2y + 3 = 0, then the line containing that point is the line to find

Detailed explanation

Straight line ∆: x – 2y + 3 = 0 has a VTPT of $$\overrightarrow n = (1; – 2)$$.

Straight line d parallel to ∆ take $$\overrightarrow n = (1; – 2)$$ as VTPT and have VTCP as $$\overrightarrow u$$ satisfying $$\overrightarrow u .\overrightarrow n = 0$$

(Type C, D)

Check points USA(-1; 1) belongs to the line $$\left\{ \begin{array}{l}x = – 1 + 2t\\y = 1 + t\end{array} \right.$$. We see the coordinates USA satisfy PT x – 2y + 3 = 0 so M lies on (Type A)

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