Question

reasoning

1. $overline{ab}$ passes through $a(-2,3)$ and $b(4,6)$.

(a) plot $a$ and $b$ and draw $overline{ab}$.
(b) point $c$, at $c(4,2)$, does not lie on $overline{ab}$. plot and label $c$. according to the parallel - line postulate, how many lines can be drawn through $c$ that are parallel to $overline{ab}$? one line
(c) draw all the lines that pass through $c$ and are parallel to $overline{ab}$. (hint: think about the slope of $overline{ab}$.)
n - gen math geometry - unit 1 - beginning concepts - lesson 11
cmathinstruction, red hook, ny 12571, © 2023

Explanation:

Step1: Plot points A and B

On the coordinate - plane, mark point A at (-2,3) and point B at (4,6), then draw the line segment $\overline{AB}$.

Step2: Plot point C

Mark point C at (4,2) on the same coordinate - plane.

Step3: Recall the Parallel Line Postulate

The Parallel Line Postulate states that through a point not on a given line, there is exactly one line parallel to the given line. Since point C(4,2) is not on $\overline{AB}$, there is one line through C that is parallel to $\overline{AB}$.

Step4: Draw the parallel line

To draw the line through C parallel to $\overline{AB}$, first find the slope of $\overline{AB}$ using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)=(-2,3)$ and $(x_2,y_2)=(4,6)$. So $m=\frac{6 - 3}{4-(-2)}=\frac{3}{6}=\frac{1}{2}$. Then, using the point - slope form of a line $y - y_1=m(x - x_1)$ with the point C(4,2) and $m = \frac{1}{2}$, we can draw the line.

Answer:

(a) Points A and B are plotted and $\overline{AB}$ is drawn. Point C is plotted.
(b) One line.
(c) The line through C with the same slope as $\overline{AB}$ (slope = $\frac{1}{2}$) is drawn.