Question

The vertices of the image of GHJK after a translation are given. Choose the vector that describes the translation.

Answer 1

Answer:

Option B

Step-by-step explanation:

Let's take a vertex G of quadrilateral GHJK to understand the rule for the translation,

From the graph attached,

Coordinates of G → (-5, 5)

Coordinates of the image point G' after the translation → G'(-5, 5)

Let the point G is translated 'a' units to the right and 'b' units down,

Rule for this translation,

G(x, y) → G'(x + a, y - a)

By this rule,

G(-5, 5) → G'(-5 + a, 5 - a)

-5 + a = -5 ⇒ a = 0

5 - a = 5 ⇒ a = 0

Therefore, vector that defines the translation will be,

<0, 0>

Option B is the the correct option.

Answer 2

The vector that describes the translation of the image is: b. (0, 0).

Recall the rules of translation:

• The image attached below shows how an image is translated using a rule.

• In the image, since we are down to the right, the rule for the translation is given as: $(x + x_1, y - y_1)$, where $a$ = units moved to the right, and $b =$ units moved downwards.

Thus, from the image given to us showing the image of GHJK, using one of the vertex J' (-3, 3) and the translation rule, $(x + a, y - b)$, the vector describing the translation can be determined as follows:

The coordinates of vertex J = (-3, 3)

$x = -3 \\\\ y = 3$

• Substitute

$J(-3, 3) = (-3 + a, 3 - b)\\\\-3 = -3 + a\\\\-3 + 3 = a\\\\\mathbf{0 = a} \\\\\\3 = 3 + b\\\\3 - 3 = b\\\\\mathbf{0 = b}$

Therefore, the vector that describes the translation of the image is: b. (0, 0).

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