Worksheet: Dilations on the Coordinate Plane

In this worksheet, we will practice finding the coordinates of the vertices of an image after dilation given the scale factor by using origin-centered dilation.

Q1:

Dilate triangle 𝐴 𝐵 𝐶 from the origin by a scale factor of 2, and state the coordinates of the image.

  • A ( 2 , 0 ) , ( 1 , 2 ) , ( 1 , 3 )
  • B ( 0 , 4 ) , ( 2 , 1 ) , ( 3 , 1 )
  • C ( 4 , 0 ) , ( 2 , 2 ) , ( 2 , 3 )
  • D ( 0 , 4 ) , ( 4 , 2 ) , ( 6 , 2 )
  • E ( 4 , 0 ) , ( 2 , 4 ) , ( 2 , 6 )

Q2:

Triangle 𝐴 𝐵 𝐶 has been dilated from point 𝐷 to triangle 𝐴 𝐵 𝐶 and, hence, the two triangles must be similar. What do you notice about the measures of the angles in both shapes?

  • A The measures were halved.
  • BThe measures were divided by three.
  • C They are equal.
  • D The measures doubled.
  • E The measures tripled.

Q3:

The figure shows two triangles: 𝐴 𝐵 𝐶 and 𝐴 𝐵 𝐶 .

Describe the single transformation that would map 𝐴 𝐵 𝐶 onto 𝐴 𝐵 𝐶 .

  • Aa translation of one up and two right
  • B a dilation from point ( 1 , 2 ) by a scale factor of 2
  • C a dilation from point ( 2 , 1 ) by a scale factor of 2
  • Da dilation from point ( 3 , 0 ) by a scale factor of 2
  • Ea translation of one up and one right

Hence, determine whether triangles 𝐴 𝐵 𝐶 and 𝐴 𝐵 𝐶 are similar.

  • AThey are similar.
  • BThey are not similar.

Q4:

Does a dilation exist that would map triangle 𝐴 𝐵 𝐶 to triangle 𝐹 𝐷 𝐸 ? If yes, state the scale factor.

  • A yes, a dilation by a scale factor of 6
  • B yes, a dilation by a scale factor of 2
  • C yes, a dilation by a scale factor of 3
  • DNo dilation exists.
  • E yes, a dilation by a scale factor of 4

Q5:

Dilate triangle 𝐴 𝐵 𝐶 from the origin by a scale factor 2, and state the coordinates of the image.

  • A ( 2 , 5 ) , ( 4 , 3 ) , ( 0 , 2 )
  • B ( 4 , 1 0 ) , ( 8 , 6 ) , ( 0 , 4 )
  • C ( 1 0 , 4 ) , ( 6 , 8 ) , ( 4 , 0 )
  • D ( 5 , 2 ) , ( 3 , 4 ) , ( 2 , 0 )
  • E ( 1 0 , 4 ) , ( 6 , 8 ) , ( 4 , 0 )

Q6:

Dilate the square 𝐴 𝐵 𝐶 𝐷 from the origin by a scale factor of 1 2 , and state the coordinates of the image.

  • A ( 3 , 2 ) , ( 5 , 2 ) , ( 5 , 6 ) , ( 3 , 6 )
  • B ( 3 , 1 ) , ( 5 , 1 ) , ( 5 , 3 ) , ( 3 , 3 )
  • C ( 6 , 1 ) , ( 1 0 , 1 ) , ( 1 0 , 3 ) , ( 6 , 3 )
  • D ( 6 , 2 ) , ( 1 0 , 2 ) , ( 1 0 , 6 ) , ( 6 , 6 )
  • E ( 1 , 3 ) , ( 1 , 5 ) , ( 3 , 5 ) , ( 3 , 3 )

Q7:

The quadrilateral 𝐴 𝐵 𝐶 𝐷 in the given figure has been dilated from the center point 𝑥 to the quadrilateral 𝐴 𝐵 𝐶 𝐷 . What is the scale factor of the dilation?

  • A 1 2
  • B1
  • C2
  • D 2
  • E 1 2

Q8:

Find the images of the vertices of the quadrilateral 𝐴 𝐵 𝐶 𝐷 after a dilation with center 𝐶 by a scale factor of 9 1 0 .

  • A 𝐴 2 3 1 0 , 1 3 1 0 , 𝐵 2 3 1 0 , 4 , 𝐶 9 2 , 1 8 5 , 𝐷 5 , 2 5
  • B 𝐴 3 6 5 , 6 3 1 0 , 𝐵 3 6 5 , 1 8 5 , 𝐶 ( 5 , 4 ) , 𝐷 9 2 , 3 6 5
  • C 𝐴 7 7 1 0 , 6 7 1 0 , 𝐵 7 7 1 0 , 4 , 𝐶 ( 5 , 4 ) , 𝐷 5 , 3 8 5
  • D 𝐴 3 6 5 , 6 3 1 0 , 𝐵 3 6 5 , 1 8 5 , 𝐶 9 2 , 1 8 5 , 𝐷 9 2 , 3 6 5
  • E 𝐴 2 7 1 0 , 2 7 1 0 , 𝐵 2 7 1 0 , 4 , 𝐶 ( 5 , 4 ) , 𝐷 5 , 1 8 5

Q9:

Triangle 𝐿 𝑀 𝑁 is transformed into triangle 𝐴 𝐵 𝐶 using a dilation centered on the origin. What is the scale factor?

  • A 1 2
  • B 1 3
  • C 2 3
  • D 3 2
  • E3

Q10:

Dilate the rectangle 𝐴 𝐵 𝐶 𝐷 from the origin by a scale factor of 1 3 , and state the coordinates of the image.

  • A ( 6 , 3 ) , ( 3 , 3 ) , ( 3 , 9 ) , ( 6 , 9 )
  • B ( 6 , 1 ) , ( 3 , 1 ) , ( 3 , 3 ) , ( 6 , 3 )
  • C ( 1 , 2 ) , ( 1 , 1 ) , ( 3 , 1 ) , ( 3 , 2 )
  • D ( 2 , 1 ) , ( 1 , 1 ) , ( 1 , 3 ) , ( 2 , 3 )
  • E ( 3 , 3 ) , ( 1 , 3 ) , ( 1 , 9 ) , ( 2 , 9 )

Q11:

Dilate triangle 𝐴 𝐵 𝐶 from the point (5, 6) by a scale factor of 2, and state the coordinates of the image.

  • A ( 4 , 3 0 ) , ( 1 0 , 4 ) , ( 2 , 6 )
  • B ( 1 , 2 ) , ( 5 , 2 ) , ( 3 , 6 )
  • C ( 4 , 6 ) , ( 1 0 , 8 ) , ( 2 , 1 2 )
  • D ( 2 , 1 ) , ( 2 , 5 ) , ( 6 , 3 )
  • E ( 2 , 3 ) , ( 5 , 4 ) , ( 1 , 6 )

Q12:

Dilate triangle 𝐴 𝐵 𝐶 from the origin by a scale factor of 1 2 , and state the coordinates of the image.

  • A ( 2 , 0 ) , ( 0 , 2 ) , ( 2 , 2 )
  • B ( 0 , 2 ) , ( 2 , 0 ) , ( 2 , 2 )
  • C ( 4 , 0 ) , ( 0 , 2 ) , ( 4 , 2 )
  • D ( 4 , 0 ) , ( 0 , 4 ) , ( 4 , 4 )
  • E ( 2 , 0 ) , ( 0 , 4 ) , ( 2 , 4 )

Q13:

The triangle 𝐴 𝐵 𝐶 in the given figure has been dilated from the center point 𝐷 to the triangle 𝐴 𝐵 𝐶 . What is the scale factor of the dilation?

Q14:

Points ( 2 , 1 ) , ( 5 , 8 ) , ( 1 , 4 ) , and ( 6 , 8 ) are the vertices of a polygon. List their images after a dilation with scale factor 1 2 .

  • A 3 2 , 3 2 , 1 1 2 , 1 7 2 , 3 2 , 7 2 , 1 1 2 , 1 5 2
  • B ( 1 , 1 ) , 5 2 , 8 , 1 2 , 4 , ( 3 , 8 )
  • C 1 , 1 2 , 5 2 , 4 , 1 2 , 2 , ( 3 , 4 )
  • D ( 1 , 1 ) , 5 2 , 8 , 1 2 , 2 , ( 3 , 4 )
  • E 3 2 , 3 2 , 1 1 2 , 1 7 2 , 1 2 , 4 , ( 3 , 8 )

Q15:

Determine the images of the vertices of 𝐽 𝐾 𝐿 after a dilation with a scale factor of 3.

  • A 𝐽 ( 3 , 2 1 ) , 𝐾 ( 2 1 , 1 2 ) , 𝐿 ( 5 , 5 )
  • B 𝐽 ( 4 , 1 0 ) , 𝐾 ( 1 0 , 7 ) , 𝐿 ( 5 , 5 )
  • C 𝐽 ( 2 1 , 3 ) , 𝐾 ( 1 2 , 2 1 ) , 𝐿 ( 6 , 6 )
  • D 𝐽 ( 4 , 1 0 ) , 𝐾 ( 2 1 , 1 2 ) , 𝐿 ( 6 , 6 )
  • E 𝐽 ( 3 , 2 1 ) , 𝐾 ( 2 1 , 1 2 ) , 𝐿 ( 6 , 6 )

Q16:

List the vertices of 𝐽 𝐾 𝐿 after a dilation with scale factor 3 4 .

  • A 𝐽 9 4 , 1 5 4 , 𝐾 2 1 4 , 9 4 , 𝐿 1 9 4 , 2 5 4
  • B 𝐽 1 5 4 , 1 7 4 , 𝐾 2 1 4 , 9 4 , 𝐿 3 , 2 1 4
  • C 𝐽 1 5 4 , 9 4 , 𝐾 9 4 , 2 1 4 , 𝐿 2 1 4 , 3
  • D 𝐽 9 4 , 1 5 4 , 𝐾 2 1 4 , 9 4 , 𝐿 3 , 2 1 4
  • E 𝐽 1 5 4 , 1 7 4 , 𝐾 3 1 4 , 9 4 , 𝐿 1 9 4 , 2 5 4

Q17:

Quadrilateral 𝐿 𝑀 𝑁 𝑃 is transformed to 𝐴 𝐵 𝐶 𝐷 using a dilation. What is the scale factor?

  • A 3 2
  • B2
  • C 1 3
  • D 2 3
  • E 1 2

Q18:

𝐴 𝐵 has been dilated from the point 𝐶 to the image 𝐴 𝐵 as seen in the figure. What is the scale factor of the dilation?

  • A 1 6
  • B 1 5
  • C5
  • D 5
  • E 1 5

Q19:

What is the image of the point with coordinates ( 𝑥 , 𝑦 ) under a dilation, centered at the origin, with scale factor 𝑘 ?

  • A ( 𝑥 + 𝑘 , 𝑦 + 𝑘 )
  • B ( 𝑥 + 𝑘 , 𝑦 𝑘 )
  • C ( 𝑥 𝑘 , 𝑦 𝑘 )
  • D 𝑥 𝑘 , 𝑦 𝑘
  • E ( 𝑥 𝑘 , 𝑦 + 𝑘 )

Q20:

Describe the geometric transformation that occurs when numbers in the complex plane are mapped to their product with 5 𝜋 2 + 𝑖 𝜋 2 c o s s i n .

  • Aa dilation with center the origin and scale factor 5 combined with a rotation by an angle of 𝜋 2 clockwise about the origin
  • Ba dilation with center the origin and scale factor 5 combined with a rotation by an angle of 𝜋 2 counterclockwise about the origin
  • Ca dilation with center the origin and scale factor 1 5 combined with a rotation by an angle of 𝜋 2 counterclockwise about the origin
  • Da dilation with center the origin and scale factor 1 5 combined with a rotation by an angle of 𝜋 2 clockwise about the origin
  • Ea dilation with center the origin and scale factor 5 2 combined with a rotation by an angle of 𝜋 2 counterclockwise about the origin

Q21:

What is the name of the transformation that changes the size of a given figure by a particular scale factor?

  • Arotation
  • Bdilation
  • Creflection
  • Dtranslation
  • Ehorizontal stretching

Q22:

Consider two circles with different radii. One of the circles can be translated so that they are concentric. Which of the following transformations could be used to transform the radius of one circle to the other?

  • A rotation
  • B translation
  • C dilation
  • D reflection

Q23:

Circle 𝐵 is a dilation of circle 𝐴 . What is the scale factor of the dilation?

Q24:

Circle 𝐵 is a dilation of circle 𝐴 . What is the scale factor of the dilation?

  • A 3 4
  • B 1 2
  • C 1 3
  • D 2 3
  • E 1 4

Q25:

Triangle 𝐴 𝐵 𝐶 has been dilated from point 𝐷 to triangle 𝐴 𝐵 𝐶 and, hence, the two triangles must be similar.

What is the scale factor of the dilation?

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.