Question

The vertices of a triangle are as follows: (4,) (6,7) and (8,0) If you dilate the triangle by a scale factor of 3, what are the vertices of the new triangle
1. (12,12) (6,7) (24,3)
2. (4,12) (6,21) (8,0)
3. (12,4) (18,7) (24,0)
4. (12,12) (18,21) (24,0)

Answer 1

Given:

Consider the vertices of the triangle are (4,4) (6,7) and (8,0).

The triangle is dilated by a scale factor of 3.

To find:

The vertices of the new triangle after dilation.

Solution:

If a figure is dilated by scale factor k with origin as the center of dilation, then the rule of dilation is:

$(x,y)\to (kx,ky)$

The given figure is dilated by scale factor 3 with origin as the center of dilation, then the rule of dilation is:

$(x,y)\to (3x,3y)$

Let the vertices of the triangle are A(4,4), B(6,7) and C(8,0).

Using this rule of dilation, we get

$A(4,4)\to A'(3(4),3(4))$

$A(4,4)\to A'(12,12)$

Similarly,

$B(6,7)\to B'(3(6),3(7))$

$B(6,7)\to B'(18,21)$

And,

$C(8,0)\to C'(3(8),3(0))$

$C(8,0)\to C'(24,0)$

The vertices of the new triangle are (12,12), (18,21), (24,0).

Therefore, the correct option is 4.