Sure, let's break this down into steps:
Step 1: Identify the Direction of the Translation
The problem states that there is a translation that is "1 unit to the left and 6 units up". A translation involves moving every point of a figure in a direction by a certain distance, without changing the shape or size of the figure. When we say "to the left", we are indicating a horizontal translation. When we say "up", we're indicating a vertical movement.
Step 2: Identify the Numerical Value of the Translation
The problem states that the translation is "1 unit to the left and 6 units up". This gives us the number of units for both our leftward (horizontal) movement and our upward (vertical) movement.
- In the horizontal case, a leftward movement is usually represented by a negative number. So "1 unit to the left" translates to -1 units. This is because on a number line or coordinate plane, we usually assume that movement to the right is positive and to the left is negative.
- In the vertical case, an upward movement is usually represented by a positive number. So "6 units up" translates to +6 units. This is because on a number line or coordinate plane, we usually assume that movement upwards is positive and downwards is negative.
Step 3: Represent the Translation as an Ordered Pair
In mathematics, especially in the Cartesian coordinate system, we usually represent movements and locations using ordered pairs (x, y), where x represents the horizontal position or movement and y represents the vertical position or movement.
So, the ordered pair that represents the given translation "1 unit to the left and 6 units up" is (-1, 6).