Question

graph the image of square jklm after a translation 5 units up.

Explanation:

Step1: Identify original coordinates

First, find the coordinates of square \(JKLM\). Let's assume the grid has each square as 1 unit. From the graph, let's find the coordinates:

• \(J\): Let's say original coordinates (estimating from the grid) – looking at the y - axis (vertical) and x - axis (horizontal). Wait, the axes: the vertical axis (probably y - axis) and horizontal (x - axis). Wait, the labels: the top axis is y (from - 10 to 10), right axis is y? Wait, no, the standard coordinate system: x - axis horizontal (right - left), y - axis vertical (up - down). Wait, in the graph, the top arrow is y (labeled - 10 to 10), right arrow is y? Wait, maybe the axes are labeled with y on the top (vertical) and x on the bottom (horizontal). Let's re - orient:

Looking at the square \(JKLM\):

Let's find the coordinates of each vertex:

• \(J\): Let's see, from the grid, if we take the horizontal (x - axis? No, maybe the horizontal is y - axis? Wait, the problem says "translation 5 units up". So "up" is along the vertical direction (y - axis, assuming y increases upwards).

Let's assume the original coordinates (before translation) of the square's vertices:

Looking at the square:

• \(J\): Let's say its coordinates are \((-9, 5)\) (wait, no, the grid lines: each grid is 1 unit. Let's check the y - axis (vertical) labels: from - 10 to 10, and x - axis (horizontal) from - 10 to 10. Wait, the square is on the left side. Let's list the vertices:

Let's take \(J\), \(M\), \(L\), \(K\) as the square.

Suppose:

• \(J\): \((-9, 5)\)
• \(M\): \((-8, 5)\)
• \(L\): \((-8, 4)\)
• \(K\): \((-9, 4)\)

Wait, no, the square has side length 1 (since it's a small square). Wait, maybe the original y - coordinates of the square are around 4 and 5. Wait, the problem is to translate 5 units up. So "up" means increasing the y - coordinate by 5.

Step2: Apply translation

A translation of 5 units up means we add 5 to the y - coordinate of each vertex.

Let's correctly identify the original coordinates:

Looking at the graph, the square \(JKLM\) has vertices:

• \(J\): Let's find the coordinates. Let's take the horizontal (y - axis) and vertical (x - axis)? Wait, no, standard coordinate system: x is horizontal (left - right), y is vertical (up - down). But in the graph, the top arrow is labeled with numbers - 10 to 10 (vertical), and the bottom arrow (x - axis) is also labeled - 10 to 10 (horizontal). So the vertical axis is y (up is positive y), horizontal is x (right is positive x).

So the square \(JKLM\) is in the left - hand side. Let's find the coordinates:

• \(J\): Let's say \(x=-9\), \(y = 5\) (wait, no, the y - values on the top axis: the square is at y = 4 and y = 5? Wait, the square has two vertices at y = 5 and two at y = 4 (since it's a square, side length 1). And x - values at x=-9 and x = - 8.

So:

• \(J\): \((x=-9, y = 5)\)
• \(M\): \((x=-8, y = 5)\)
• \(L\): \((x=-8, y = 4)\)
• \(K\): \((x=-9, y = 4)\)

Now, translating 5 units up: add 5 to the y - coordinate of each vertex.

• New \(J\): \((-9, 5 + 5)=(-9, 10)\)
• New \(M\): \((-8, 5 + 5)=(-8, 10)\)
• New \(L\): \((-8, 4 + 5)=(-8, 9)\)
• New \(K\): \((-9, 4 + 5)=(-9, 9)\)

Now, we need to plot these new points on the graph. The original square is at y = 4 - 5, after translation, it's at y = 9 - 10.

Step3: Plot the new square

Plot the points \((-9, 10)\), \((-8, 10)\), \((-8, 9)\), \((-9, 9)\) on the grid. These points will form the translated square, 5 units above the original square.

Answer:

To graph the image of square \(JKLM\) after a translation 5 units up, follow these steps:

1. Identify Original Vertices: Find the coordinates of each vertex of square \(JKLM\). For example, if \(J(-9, 5)\), \(M(-8, 5)\), \(L(-8, 4)\), \(K(-9, 4)\) (from the grid).
2. Apply Translation: Add 5 to the \(y\) - coordinate of each vertex (since "up" is along the \(y\) - axis).

• New \(J\): \((-9, 5 + 5)=(-9, 10)\)
• New \(M\): \((-8, 5 + 5)=(-8, 10)\)
• New \(L\): \((-8, 4 + 5)=(-8, 9)\)
• New \(K\): \((-9, 4 + 5)=(-9, 9)\)

1. Plot New Vertices: Mark the points \((-9, 10)\), \((-8, 10)\), \((-8, 9)\), \((-9, 9)\) on the grid and connect them to form the translated square.

(Note: The final graph will have the square shifted 5 units upward from its original position, with vertices at the new coordinates calculated above.)