Question

test prep

1. which figure is a translation of figure a?

a figure 1
b figure 2
c figure 3
d figure 4

1. the coordinates of a triangle are given in the table.

the triangle is translated using the rule (x, y) → (x − 3, y + 2).
what are the coordinates of the image of the triangle?
preimage coordinates | image coordinates
(0, 1) |
(2, 3) |
(4, 2) |

1. a quadrilateral is translated 5 units right and 3 units down on a coordinate plane. which expressions could be used to find one of the coordinates of the vertices of the image? select all that are correct.

a x − 3
b x − 5
c x + 5
d y − 3
e y + 3
f y + 5

spiral review

1. you and 19 other people are entered in a drawing. one person will be randomly selected to win a prize. what is the probability that you will win the prize?

1. ten red cards and ten black cards are placed in a bag. you choose one card and then another without replacing the first card. what is the probability that the first card will be red and the second card will be black?

1. seamus solves 100 randomly generated math problems that each of addition, subtraction, multiplication, or division. predict the number of division problems seamus solves.

Explanation:

Question 6

Step1: Recall translation properties

A translation preserves the shape and size of a figure, only moving it. So we check which figure has the same shape and orientation as Figure A.

Step2: Compare figures

• Figure 1: Different shape (trapezoid vs Figure A's trapezoid? Wait, Figure A is a trapezoid, Figure 1 looks similar but maybe not. Wait, Figure 3: same shape and orientation as Figure A, just moved. Figure 2 is smaller, Figure 4 is a parallelogram. So Figure 3 is the translation.

Step1: Apply translation rule

The translation rule is \((x, y) \to (x - 3, y + 2)\). So for each preimage coordinate, subtract 3 from \(x\) and add 2 to \(y\).

Step2: Calculate for each point

• For \((0, 1)\): \(x = 0 - 3 = -3\), \(y = 1 + 2 = 3\), so \((-3, 3)\)
• For \((2, 3)\): \(x = 2 - 3 = -1\), \(y = 3 + 2 = 5\), so \((-1, 5)\)
• For \((4, 2)\): \(x = 4 - 3 = 1\), \(y = 2 + 2 = 4\), so \((1, 4)\)

Step1: Recall translation directions

Translating 5 units right: for \(x\)-coordinate, we add 5 (since right is positive \(x\) direction), so \(x + 5\). Translating 3 units down: for \(y\)-coordinate, we subtract 3 (since down is negative \(y\) direction), so \(y - 3\).

Step2: Identify correct options

So the correct expressions are \(x + 5\) (option C) and \(y - 3\) (option D).

Answer:

C. Figure 3 (assuming the option for Figure 3 is labeled as such, from the original options: the option with Figure 3 is the correct one, so if the options are A. Figure 1, B. Figure 2, C. Figure 3, D. Figure 4, then the answer is C. Figure 3)

Question 7