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Point H is located at -1 . Points I and J are each 9 units away from Point H. Where are I and J located? I=◻quadJ=◻

Point H \mathrm{H} is located at −1-1 . Points I \mathrm{I} and J \mathrm{J} are each 99 units away from Point H \mathrm{H} . Where are I and J located?\newlineI=□J=□ \mathrm{I}=\square \quad \mathrm{J}=\square

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Full solution

Q. Point H \mathrm{H} is located at −1-1 . Points I \mathrm{I} and J \mathrm{J} are each 99 units away from Point H \mathrm{H} . Where are I and J located?\newlineI=□J=□ \mathrm{I}=\square \quad \mathrm{J}=\square
  1. Identify Given Information: Identify the given information and what is being asked.\newlinePoint HH is located at −1-1 on a number line. Points II and JJ are each 99 units away from Point HH. We need to find the locations of Points II and JJ.
  2. Determine Point I: Determine the location of Point I.\newlineSince Point I is 99 units away from Point H, and Point H is at −1-1, we can find Point I by either adding 99 to −1-1 or subtracting 99 from −1-1. Point I could be at −1+9=8-1 + 9 = 8 or at −1−9=−10-1 - 9 = -10.
  3. Determine Point J: Determine the location of Point J.\newlinePoint J is also 99 units away from Point H. If we consider the two possible locations for Point I, Point J will be at the opposite side of Point H. Therefore, if Point I is at 88, Point J will be at −10-10, and vice versa.
  4. Check Distances: Check the distance between Points H, I, and J to ensure they are 99 units apart.\newlineThe distance between Point H at −1-1 and Point I at 88 is ∣8−(−1)∣=∣8+1∣=9|8 - (-1)| = |8 + 1| = 9 units.\newlineThe distance between Point H at −1-1 and Point J at −10-10 is ∣−10−(−1)∣=∣−10+1∣=9|-10 - (-1)| = |-10 + 1| = 9 units.\newlineBoth distances are 99 units, so there is no math error.

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