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In this lesson, we will learn how to find 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.

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?

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 ′ .

Hence, determine whether triangles 𝐴 𝐵 𝐶 and 𝐴 ′ 𝐵 ′ 𝐶 ′ 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.

Q5:

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

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.

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?

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 .

Q9:

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

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.

Q11:

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

Q12:

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

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?

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 .

Q15:

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

Q16:

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

Q17:

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