Tomas is planning out a rail trail using a map with a marked grid. The head of the trail, which has an information kiosk, is located at (3, 0). He moves 1 unit east and 3 units north and places a pin at (4, 3) to represent the location of another information kiosk. He continues placing pins so that each pin is 1 unit east and 3 units north in relation to the previous pin. Which of the following points will have pins? Select all that apply.
A coordinate plane has an x-axis labeled East from 0 to 10 in increments of 1 and a y-axis labeled North from 0 to 10 in increments of 1.
(1 point)
Responses
(5, 6)
(5, 6)
(6, 8)
(6, 8)
(7, 10)
(7, 10)
(8, 17)
(8, 17)
(9, 18)
(9, 18)
(10, 21)
(10, 21)
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It seems like the pattern is that the x-coordinate increases by 1 and the y-coordinate increases by 3 with each pin. Let's follow this pattern to see which points will have pins:
(3, 0) -> head of the trail and information kiosk
(4, 3) -> first pin
(5, 6) -> second pin
(6, 9) -> third pin
(7, 12) -> fourth pin
(8, 15) -> fifth pin
(9, 18) -> sixth pin
(10, 21) -> seventh pin
So, the points that will have pins are (5, 6), (6, 9), (7, 12), (8, 15), (9, 18), and (10, 21).