Question 5
Using your sense of how parallel lines look, try to draw lines parallel to the line segments on this dot paper.
(a) Did you find it challenging to draw some of them? (b) Which ones? (c) How did you do it?
Parallel lines are lines that always stay the same distance apart and never meet.
Step 1 — Understanding Parallel Lines on Dot Paper
Let us look at the dot paper. Each dot is a point. Line segments connect some dots. We want to draw new lines. These new lines must be parallel. Parallel lines have the same slope. Slope tells us how steep a line is. On dot paper, we find slope by counting. We count how many dots up or down. This is called the "rise". We count how many dots right or left. This is called the "run".
Step 2 — Finding Rise and Run for a Line Segment
Let us pick a line segment. We will use line 'a' as an example. Start at the bottom-left dot of 'a'. Move to the top-right dot of 'a'. We go 1 dot up. So, the rise is 1. We go 2 dots to the right. So, the run is 2. The slope of line 'a' is 1 up for 2 right.
Let us try line 'b'. Start at the top-left dot of 'b'. Move to the bottom-right dot of 'b'. We go 3 dots down. So, the rise is -3. We go 1 dot to the right. So, the run is 1. The slope of line 'b' is 3 down for 1 right.
Let us try line 'h'. Start at the top-left dot of 'h'. Move to the bottom-right dot of 'h'. We go 2 dots down. So, the rise is -2. We go 8 dots to the right. So, the run is 8. The slope of line 'h' is 2 down for 8 right.
Step 3 — Drawing a Parallel Line
To draw a line parallel to 'a': First, find its rise and run. For 'a', the rise is 1 and the run is 2. Next, choose any other dot on the paper. This will be the start of our new line. From this new starting dot, move 1 dot up. Then move 2 dots to the right. Mark this new dot. Now, connect your starting dot to this marked dot. This new line segment is parallel to 'a'. We use the same method for all other lines. For line 'b', we would move 3 dots down and 1 dot right. For line 'h', we would move 2 dots down and 8 dots right. Some lines might be harder to count. This happens if they do not end exactly on a dot. Or if their rise and run are very large. Lines 'b', 'f', and 'h' might feel tricky. But we can still count their rise and run. Line 'f' goes 5 dots down and 2 dots right. Line 'g' goes 1 dot up and 5 dots right. Line 'e' goes 3 dots down and 1 dot right. Line 'c' goes 3 dots up and 3 dots right. Line 'd' goes 2 dots up and 2 dots right. We can simplify 'c' to 1 up and 1 right. We can simplify 'd' to 1 up and 1 right. So, 'c' and 'd' are parallel to each other.
Answer
(a) This is for you to answer after trying. You might find some challenging. (b) This is for you to answer after trying. You might find lines like 'b', 'f', or 'h' a bit harder. (c) We found the "rise" and "run" of each line segment. Then, we used the same rise and run to draw a new line from a different dot.
More questions in FIO
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