Question

Jack started from home (1, 1) and moved 8 units to the right on the x-axis and 6 units up on the y-axis to reach his office. Find the coordinates of Jack’s office and the distance from Jack’s home to his office, if one unit represents 5 miles.

• A. (8, 6), 12 mi
• B. (9, 7), 70 mi
• C. (7, 9), 70 mi
• D. (7, 9), 80 mi

Answer 1

The correct option is B (9, 7), 70 mi

Let the point representing Jack’s home be H and the point representing his office be O.
Jack started from home, i.e., H with the coordinates (1, 1).

Given:
● Jack moved 8 units to the right on the x-axis to reach his office.
Therefore, x-coordinate of O = 1 + 8 = 9
● Jack moved 6 units up on the y-axis to reach his office.
Therefore, y-coordinate of O = 1 + 6 = 7


So, the coordinates of O are (9, 7).

Since we know that Jack traveled 8 units along the x-axis and 6 units along the y-axis, the total covered by Jack

$=8+6=14\text{units}$

1 unit = 5 units

So, 14 units $=15\times 14=70mi$

Hence, the distance between Jack’s home and his office is 70 mi.