Question

16

To get to Amala's house, Tara walks 4 blocks west (left), then 3 blocks north (up), and
then 2 blocks west. Amala's house has coordinates (9,9). What are the coordinates of
Tara's starting point?
A
B.
C
D
(2,0)
(2,6)
(15,6)
(12, 2)

Answer 1

Correct answer is C. (15,6)

Explanation:

Let us think of the
`xy` co-ordinates plane. We can move in four directions.

1. North (i.e. upwards) If we move north or upwards the value of y-coordinate will increase.

2. South (i.e. downwards) If we move south or downwards the value of y-coordinate will decrease.

3. West (i.e. left) If we move west or left the value of x-coordinate will decrease.

4. East (i.e. right) If we move east or right the value of x-coordinate will increase.

Let us imagine, the starting coordinate of Tara be
`(x,y)`

Let us apply the above 4 directions and the properties in the question statement.

Step 1: Tara walks 4 blocks west (left), x coordinate will decrease by 4.

New coordinates will be
`(x-4,y)`.

Step 2: Tara walks 3 blocks north (up), y coordinate will increase by 3.

New coordinates will be
`(x-4,y+3)`.

Step 3: Tara walks 2 blocks west (left), x coordinate will decrease by 2.

New coordinates will be
`(x-4-2,y+3) \Rightarrow (x-6,y+3)`.

Now Tara is at (9,9)

Comparing the x and y coordinates:

`x-6=9\\\Rightarrow x = 15`

`y+3=9\\\Rightarrow y = 6`

So, Tara's starting point is (15,6) hence, option C is correct.