Question

practice questions grade 10 essentials lesson 39 - translations 1. translate the following shape up 4 and 1 to the right. 3. translate the shape 2 to the left and up 1. 2. translate the following shape down 5 and 3 to the left. 4. translate the shape below 8 units to the left and 6 units up. created by c. hotel and c. forsyth (2018) 85

Answer:

To solve these translation problems, we'll focus on problem 1 as an example (the process is similar for others). Let's assume the original triangle has vertices \( A \), \( B \), \( C \) with coordinates (we'll estimate from the grid, but the key is the translation vector: up 4 (add 4 to y - coordinate) and right 1 (add 1 to x - coordinate)).

Step 1: Recall the translation rules

For a translation of \( h \) units right (add \( h \) to \( x \)) and \( k \) units up (add \( k \) to \( y \)), the transformation of a point \( (x,y) \) is \( (x + h,y + k) \). Here, \( h = 1 \) (right 1) and \( k=4 \) (up 4).

Step 2: Apply the translation to each vertex

Suppose the original coordinates of a vertex (e.g., vertex \( B \)) is \( (x_0,y_0) \). After translation, the new coordinate \( (x_1,y_1)=(x_0 + 1,y_0 + 4) \). We do this for all vertices of the triangle. Then we plot the new points and connect them to get the translated shape.

For problem 2 (translate down 5 and 3 to the left):

Step 1: Translation rules

Translation down 5 means subtract 5 from the \( y \) - coordinate, and 3 to the left means subtract 3 from the \( x \) - coordinate. So for a point \( (x,y) \), the new point is \( (x - 3,y - 5) \).

Step 2: Apply to each vertex of the rectangle (with vertices \( D \), \( E \), \( F \), \( G \))

Take vertex \( D \) (assume original coordinate \( (x_D,y_D) \)). New coordinate: \( (x_D-3,y_D - 5) \). Repeat for \( E \), \( F \), \( G \) and draw the new rectangle.

For problem 3 (translate left and up 1):

Step 1: Translation rules

Left 1: subtract 1 from \( x \), up 1: add 1 to \( y \). So \( (x,y)\to(x - 1,y + 1) \).

Step 2: Apply to each vertex of the diamond (vertices \( J \), \( K \), \( L \), \( I \))

For a vertex \( (x,y) \) of the diamond, new coordinate is \( (x - 1,y + 1) \). Plot the new points.

For problem 4 (translate 8 units left and 6 units up):

Step 1: Translation rules

Left 8: subtract 8 from \( x \), up 6: add 6 to \( y \). So \( (x,y)\to(x - 8,y + 6) \).

Step 2: Apply to each vertex of the quadrilateral (vertices \( M \), \( N \), \( P \), \( Q \))

Take vertex \( M \) (assume original coordinate \( (x_M,y_M) \)). New coordinate: \( (x_M-8,y_M + 6) \). Do this for all vertices and draw the new quadrilateral.

If we were to give a general answer for the translation process:
To translate a shape:

1. Identify the translation vector (number of units left/right and up/down).
2. For each vertex \( (x,y) \) of the shape:

• If moving right \( h \) units: \( x_{\text{new}}=x + h \); if moving left \( h \) units: \( x_{\text{new}}=x - h \).
• If moving up \( k \) units: \( y_{\text{new}}=y + k \); if moving down \( k \) units: \( y_{\text{new}}=y - k \).

1. Plot the new vertices and connect them to form the translated shape.

For example, if we take a specific point from the hand - written notes (e.g., \( L(- 3,2) \) in the hand - written part, and the intended translation seems to be left 5? Wait, no, the hand - written has \( L(-3,2)\to(2,3) \), maybe a miscalculation, but following the problem's instruction:

If we take the problem - stated translations:

For problem 1 (up 4, right 1):
If a vertex is \( (x,y) \), new vertex is \( (x + 1,y + 4) \)

For problem 2 (down 5, left 3):
New vertex: \( (x-3,y - 5) \)

For problem 3 (left 1, up 1):
New vertex: \( (x - 1,y + 1) \)

For problem 4 (left 8, up 6):
New vertex: \( (x-8,y + 6) \)

The key is to apply the horizontal (x - axis: right is +, left is -) and vertical (y - axis: up is +, down is -) translation rules to each vertex of the shape and then redraw the shape.