Question 13 of 25intermediate🔧 ApplyShort Answer2 marks

Point WW has xx-coordinate equal to −5-5. Can you predict the coordinates of point HH which is on the line through WW parallel to the yy-axis? Which quadrants can HH lie in?

Correct Answer

Since point HH lies on the line through WW parallel to the y-axis, its x-coordinate will be the same as that of WW. Therefore, the xx-coordinate of HH is −5-5. The yy-coordinate of HH can be any real number, so the coordinates of HH are (−5, y)(-5,\, y).

Depending on the value of yy, point HH can lie in Quadrant II or Quadrant III. If yy is positive, the point will have a negative xx and positive yy, placing it in Quadrant II. If yy is negative, both coordinates will be negative, placing it in Quadrant III.

Exercise: END-OF-CHAPTER EXERCISES | Q: 2 | (Page 12)
For More Understanding

Explanation

A line parallel to the yy-axis has a constant xx-coordinate. Since WW has an xx-coordinate of −5-5, any point HH on this line will also have an xx-coordinate of −5-5. The yy-coordinate can vary.

Based on the quadrant rules in the text, a point with a negative xx-coordinate and positive yy-coordinate lies in Quadrant II, while a point with both negative coordinates lies in Quadrant III.

Solution Steps

  1. Step 1: Identify that a line parallel to the yy-axis has a constant xx-coordinate. Since WW has x=−5x = -5, HH must also have x=−5x = -5.

  2. Step 2: Express the coordinates of HH as (−5, y)(-5,\, y), where yy can be any real number.

  3. Step 3: Determine the quadrants based on the signs of the coordinates. A negative xx and positive yy places HH in Quadrant II. A negative xx and negative yy places HH in Quadrant III.

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