Question

graph the image of δghi after the following sequence of transformations:
reflection across the x-axis
translation 4 units left and 17 units down

Explanation:

To solve this, we first need the coordinates of \( \triangle GHI \). From the graph:

• Let's assume \( I = (8, -14) \), \( H = (10, -12) \), \( G = (12, -14) \) (since the y - axis is inverted here, lower y - values are more negative).

Step 1: Reflect across the \( x \) - axis

The rule for reflection across the \( x \) - axis is \( (x,y)\to(x, - y) \).

• For \( I(8, - 14) \): \( (8, -(-14))=(8,14) \)
• For \( H(10, - 12) \): \( (10, -(-12))=(10,12) \)
• For \( G(12, - 14) \): \( (12, -(-14))=(12,14) \)

Step 2: Translate 4 units left and 17 units down

The rule for translation 4 units left (subtract 4 from \( x \)) and 17 units down (subtract 17 from \( y \)) is \( (x,y)\to(x - 4,y - 17) \).

• For \( I(8,14) \): \( (8 - 4,14 - 17)=(4, - 3) \)
• For \( H(10,12) \): \( (10 - 4,12 - 17)=(6, - 5) \)
• For \( G(12,14) \): \( (12 - 4,14 - 17)=(8, - 3) \)

Now, plot the points \( (4, - 3) \), \( (6, - 5) \), and \( (8, - 3) \) and connect them to get the image of \( \triangle GHI \) after the transformations.

(Note: If the initial coordinates were misread, adjust the reflection and translation accordingly. The key is to apply the reflection rule \( (x,y)\to(x, - y) \) first, then the translation rule \( (x,y)\to(x - 4,y - 17) \) to each vertex of the triangle.)

To graph:

1. Mark the reflected points first, then apply the translation.
2. The final triangle will have vertices at \( (4, - 3) \), \( (6, - 5) \), and \( (8, - 3) \).

(If you need to draw on the grid, locate these points: \( (4, - 3) \) is 4 units right on the x - axis and 3 units down on the y - axis, \( (6, - 5) \) is 6 units right and 5 units down, \( (8, - 3) \) is 8 units right and 3 units down. Connect these three points.)

Answer:

To solve this, we first need the coordinates of \( \triangle GHI \). From the graph:

• Let's assume \( I = (8, -14) \), \( H = (10, -12) \), \( G = (12, -14) \) (since the y - axis is inverted here, lower y - values are more negative).

Step 1: Reflect across the \( x \) - axis

The rule for reflection across the \( x \) - axis is \( (x,y)\to(x, - y) \).

• For \( I(8, - 14) \): \( (8, -(-14))=(8,14) \)
• For \( H(10, - 12) \): \( (10, -(-12))=(10,12) \)
• For \( G(12, - 14) \): \( (12, -(-14))=(12,14) \)

Step 2: Translate 4 units left and 17 units down

The rule for translation 4 units left (subtract 4 from \( x \)) and 17 units down (subtract 17 from \( y \)) is \( (x,y)\to(x - 4,y - 17) \).

• For \( I(8,14) \): \( (8 - 4,14 - 17)=(4, - 3) \)
• For \( H(10,12) \): \( (10 - 4,12 - 17)=(6, - 5) \)
• For \( G(12,14) \): \( (12 - 4,14 - 17)=(8, - 3) \)

Now, plot the points \( (4, - 3) \), \( (6, - 5) \), and \( (8, - 3) \) and connect them to get the image of \( \triangle GHI \) after the transformations.

(Note: If the initial coordinates were misread, adjust the reflection and translation accordingly. The key is to apply the reflection rule \( (x,y)\to(x, - y) \) first, then the translation rule \( (x,y)\to(x - 4,y - 17) \) to each vertex of the triangle.)

To graph:

1. Mark the reflected points first, then apply the translation.
2. The final triangle will have vertices at \( (4, - 3) \), \( (6, - 5) \), and \( (8, - 3) \).

(If you need to draw on the grid, locate these points: \( (4, - 3) \) is 4 units right on the x - axis and 3 units down on the y - axis, \( (6, - 5) \) is 6 units right and 5 units down, \( (8, - 3) \) is 8 units right and 3 units down. Connect these three points.)