Question

"The distance between which of these pairs of points is 9 units?"

a) (-8, 11) and (-2, 11)
b) (-1, 5) and (-1, 14)
c) (7, -2) and (15, -2)
d) (4, -6) and (4, 15)

Answer 1

The pair of points with a distance of exactly 9 units is b) (-1, 5) and (-1, 14), as they are positioned along a vertical line with the y-coordinate having a difference of 9 units.

Step-by-step explanation:

The question asks to determine the distance between pairs of points that is exactly 9 units.

To calculate the distance between two points in a coordinate system, we use the distance formula. However, by observing the coordinates, we can see in each pair of points whether they lie on a horizontal or vertical line, and thus determine the distance directly without the need for calculations.

• Option a) (-8, 11) and (-2, 11), we can see that the x-coordinates change while the y-coordinate remains the same, implying a horizontal line. The distance is |-8 - (-2)| = |-8 + 2| = | -6 | = 6 units, which is not equal to 9 units.
• Option b) (-1, 5) and (-1, 14), here the y-coordinates change while the x-coordinate remains constant, indicating a vertical line. The distance is |5 - 14| = |-9| = 9 units. This is the pair with a distance of 9 units.
• Option c) (7, -2) and (15, -2), similarly shows a horizontal line with the distance calculated as |7 - 15| = |-8| = 8 units, not 9 units.
• Option d) (4, -6) and (4, 15), this shows a vertical line with distance | -6 - 15| = |-21| = 21 units, which is also not equal to 9 units.