DCA #1 Reteach

Multiple Choice

A circle is graphed on a coordinate grid with its center at (9, -4).  The circle will be translated g units to the right and h units down.

Which rule describes the center of the new circle after this translation?

• x, y) → (9 - g, -4 - h)

• (x, y) → (9 + g, -4 - h)

• (x, y) → (9 - g, -4 + h)

• (x, y) → (9 + g, -4 + h)

The y-axis lies vertically, going up and down. The numbers above zero are positive so you add. The numbers are below zero are negative so you aubstract.

El eje y se encuentra verticalmente, subiendo y bajando. Los números encima de cero son positivos, por lo que se suman. Los números que están debajo de cero son negativos, por lo que se resta.

Y-values

The x-axis lies horizontally, going left and right. The numbers to the left are negative so you have to subtract. The numbers to the right are positive so you add.

El eje x es horizontal y va de izquierda a derecha. Los números de la izquierda son negativos por lo que hay que restarlos. Los números de la derecha son positivos, así que sumas.

X-values

This is translation

Multiple Choice

Trapezoid ABCD is reflected over the x-axis to form trapezoid WXYZ.

Which statement is true?

• The angle measures of trapezoid ABCD are less than the corresponding angle measures of trapezoid WXYZ.

• The sum of the angle measures of trapezoid ABCD is twice the sum of the angle measures of trapezoid WXYZ.

• The side lengths of trapezoid ABCD are congruent to the corresponding side lengths of trapezoid WXYZ.

• The area of trapezoid ABCD is greater than the area of trapezoid WXYZ.

Rigid Transformations

Reflection is a rigid transformation. That means the shape is congruent. Congruent means same shape and size. The side lengths and angles are congruent.

La reflexión es una transformación rígida. Eso significa que la forma es congruente. Congruente significa misma forma y tamaño. Las longitudes de los lados y los ángulos son congruentes.

Multiple Choice

A figure is reflected over the x-axis.  Which rule below describes this transformation?

• (x,y)

  →

  (-y,-x)

• (x,y)

  →

  (y,x)

• (x,y)

  →

  (-x,y)

• (x,y)

  →

  (x,-y)

Reflection

Reflection is a flip. When you flip over the x-axis, you change the y-value. When you flip over the y-axis, you change the x-axis. Remember the negative means change to the opposite.

The reflection is a mirror. When you reflect on the x-axis, you change the value of y. When you reflect on the y-axis, you change the x-axis. Remember that negative means changing to the opposite.

Drag and Drop

The table describes two dilations with the center of dilation at the origin. Which rule describes a dilation?

be used.​ ​ ​

Placeholder

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Placeholder

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Drag these tiles and drop them in the correct blank above

(x,y)--> (1/4x, 1/4y)

(x,y)-->(x+4,y+4)

(x,y)-->(x+1/4, y+1/4)

(x,y)-->(4x,4y)

Dilation

Dilation is when a shape gets bigger or smaller. The rule for dilation should have the scale factor or k. Dilation is about multiplication.

La dilatación es cuando una forma se hace más grande o más pequeña. La regla para la dilatación debe tener el factor de escala o k. La dilatación se trata de multiplicación.

Multiple Choice

A triangle is graphed on a coordinate grid. Which transformation will result in a triangle that is NOT congruent to the original triangle?

• A translation 10 units to the left

• A rotation of 270° counterclockwise

• A dilation by a scale factor of 1/3

• A reflection across the y-axis

Rigid vs. Non-Rigid Transformations

Rigid means congruent. The only non-rigid or not congruent transformation is dilation because the size of the figure changes.

Rígido significa congruente. La única transformación no rígida o no congruente es la dilatación porque el tamaño de la figura cambia.

Dropdown

Figure JKLMN is reflected across the x-axis to form figure J'K'L'M'N'.

Select the answers that are true.

​ ​

Select answer

​ ​

Select answer

Reflection

The shape was reflected across the x-axis so the y-value changed to its opposite. The rule should be (x,y)-->(x,-y). The negative means change to the opposite.

La forma se reflejó a lo largo del eje x, por lo que el valor y cambió a su opuesto. La regla debería ser (x,y)-->(x,-y). Negativo significa cambiar hacia lo contrario.

Multiple Choice

The coordinate grid shows triangle STU.

Triangle STU is rotated 90^o clockwise about the origin to create triangle S'T'U'.  Which rule describes this transformation?

• (x,y)

  →

  (x,-y)

• (x,y)

  →

  (-y,x)

• (x,y)

  →

  (-x,y)

• (x,y)

  →

  (y,-x)

Rotation

You should be using your arrow rule to figure out the rules for 90^o, 180^o, and 270^o clockwise and counterclockwise. Remember the rule for 90^o clockwise is the same as 270^o counterclockwise.

Debes usar la regla de las flechas para descubrir las reglas para 90°, 180° y 270° en el sentido de las agujas del reloj y en el sentido contrario a las agujas del reloj. Recuerde que la regla para 90° en el sentido de las agujas del reloj es la misma que 270° en el sentido contrario a las agujas del reloj.

Multiple Choice

A rectangle is graphed on a coordinate plane. The table shows the original vertices and the new vertices after a scale factor with center of dilation at (0,0) is applied.

Vertice of Original Rectangle: (2,4)

Vertice of New Rectangle: (5,10)

What rule is applied to the original rectangle to create the new rectangle?

• (x,y)-->(x+2,y+5)

• (x,y)-->(2/5x,2/5y)

• (x,y)-->(5/2x,5/2y)

• (x,y)-->(x-2,y-5)

Dilation with 2 points

When you are given two points and DO NOT have a scale factor, you will need to divide 2 numbers. The two X's or the two Y's. Remember, it is the new number divided by the old number.

Cuando te dan dos puntos y NO tienes un factor de escala, necesitarás dividir dos números: las dos X o las dos Y. Recuerda, es el nuevo número dividido por el número anterior.

Multiple Choice

Figure ABCDE is shown on a coordinate grid. It is dilated with the origin as the center of dilation to create figure A'B'C'D'E'.

If figure ABCDE were dilated using the rule

(x,y)→(1/5​x,1/5​y),

What would the x-coordinate of A' be?

• 1

• -5

• 5

• -1

Dilation with a scale factor

When you are given an original point and a scale factor, you need to multiply the original numbers with the scale factor ONE AT A TIME. You take the x-coordinate times the scale factor and the y-coordinate times the scale factor to get two new numbers.

Cuando se da un punto original y un factor de escala, los números originales deben multiplicarse por el factor de escala UNO A LA VEZ. La coordenada x se multiplica por el factor de escala y la coordenada y se multiplica por el factor de escala para obtener dos números nuevos.

Multiple Choice

Pentagon ABCDE is shown on the coordinate grid.  Pentagon ABCDE is dilated with the origin as the center of dilation using the rule (x,y)→(1/4x,1/4y)

 to create pentagon A'B'C'D'E'.

Which statement is true?

• Pentagon A'B'C'D'E' is smaller than pentagon ABCDE, because the scale factor is less than 1.

• Pentagon A'B'C'D'E' is larger than pentagon ABCDE, because the scale factor is less than 1.

• Pentagon A'B'C'D'E' is larger than pentagon ABCDE, because the scale factor is greater than 1.

• Pentagon A'B'C'D'E' is smaller than pentagon ABCDE, because the scale factor is greater than 1.

Scale Factor

Remember to put your scale factor in the calculator if it is a fraction. Anything less one, the shape will get smaller. Anything bigger than one, the shape will get bigger.

Recuerda introducir el factor de escala en tu calculadora si estás trabajando con una fracción. Si el valor es menor que uno, la cifra será menor. Si el valor es mayor que uno, la cifra será mayor.

Multiple Choice

Yolanda and her mom make greeting cards to send to family and friends. Yolanda designs a card that measures 3 inches by 5 inches. The card is represented by figure ABCD. She enlarges the card to form image A'B'C'D'. She uses a scale factor of 4 with a center of dilation at the origin. What are the coordinates of B'?

• (3,5)

• (12,5)

• (7,9)

• (12,20)

Scale Factor on a Graph

You should have found the x-coordinate and y-coordinate of point B. Then you needed to multiply both of those numbers by the scale factor of 4.

Deberías haber encontrado la coordenada x y la coordenada y del punto B. Luego deberías haber multiplicado ambos números por el factor de escala de 4.

Multiple Choice

You can identify the coordinates of the vertices of the image in the coordinate plane.

Make a table to compare corresponding vertices of Triangle PQR and Triangle P'Q'R'.

Triangle PQR Vertices:

P(1,-1), Q(3,-2), R(2,-4)

What are the new vertices of the triangle?

• P(1,-1), Q(3,-2), R(2,-4)

• P(1,1), Q(2,3), R(4,2)

• P(-1,-1), Q(-3,-2), R(-2,-4)

Rotation on a Graph

With this question, you just needed to look at the graph to find the new points.

Con esta pregunta sólo necesitabas mirar la gráfica para encontrar los nuevos puntos.

Multiple Choice

Triangle DEF is shown on the coordinate plane below.  It is transformed using the rule 

(x,y)→(x+6,y−3).

Which of the following describes this transformation?

• A translation 6 units down and 3 units left

• A translation 6 units up and 3 units to the left

• A translation 6 units to the right and 3 units down

• A translation 6 units to the left and 3 units up

Multiple Choice

 A figure is transformed using the rule 

(x,y)→(−x,y).

Which of the following best describes the transformation?

• A 90°

  clockwise rotation about the origin

• A reflection across the x-axis

• A translation 1 unit to the left

• A reflection across the y-axis