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Lesson: Dilations on the Coordinate Plane

Sample Question Videos

Worksheet • 20 Questions • 1 Video

Q1:

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

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

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

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

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

  • AThey are not similar.
  • BThey are 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 2
  • BNo dilation exists.
  • C yes, a dilation by a scale factor of 4
  • D yes, a dilation by a scale factor of 6
  • E yes, a dilation by a scale factor of 3

Q5:

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

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

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 , 1 ) , ( 5 , 1 ) , ( 5 , 3 ) , ( 3 , 3 )
  • B ( 6 , 1 ) , ( 1 0 , 1 ) , ( 1 0 , 3 ) , ( 6 , 3 )
  • C ( 6 , 2 ) , ( 1 0 , 2 ) , ( 1 0 , 6 ) , ( 6 , 6 )
  • D ( 3 , 2 ) , ( 5 , 2 ) , ( 5 , 6 ) , ( 3 , 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 centre point 𝑥 to the quadrilateral 𝐴 𝐵 𝐶 𝐷 . What is the scale factor of the dilation?

  • A 1 2
  • B1
  • C 1 2
  • D2
  • E 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 7 7 1 0 , 6 7 1 0 , 𝐵 7 7 1 0 , 4 , 𝐶 ( 5 , 4 ) , 𝐷 5 , 3 8 5
  • B 𝐴 2 7 1 0 , 2 7 1 0 , 𝐵 2 7 1 0 , 4 , 𝐶 ( 5 , 4 ) , 𝐷 5 , 1 8 5
  • C 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
  • D 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
  • E 𝐴 3 6 5 , 6 3 1 0 , 𝐵 3 6 5 , 1 8 5 , 𝐶 ( 5 , 4 ) , 𝐷 9 2 , 3 6 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 2 3
  • B3
  • C 3 2
  • D 1 2
  • E 1 3

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

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

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 , 4 ) , ( 4 , 4 )
  • D ( 4 , 0 ) , ( 0 , 2 ) , ( 4 , 2 )
  • E ( 2 , 0 ) , ( 0 , 4 ) , ( 2 , 4 )

Q13:

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

  • A3
  • B4
  • C 1 3
  • D 3
  • E 1 3

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

Q17:

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