Question

Suppose Triangle MNO has vertices M(-7,3), N(9,8), and 0(2,16). After a dilation centered at the origin, the coordinates of Triangle M'N'O are M'(-10.5, 4.5), N' (13.5, 12), and O' (3, 24). Complete the following algebraic description so that it represents the transformation of Triangle MNO, (, y) = (2_1_, Y -) The scale factor is

Answer 1

The triangle MNO

M(-7,3)

N(9,8)

O(2,16)

Was dilated with respect of the origin resulting the triangle M'N'O'

M'(-10.5,4.5)

N'(13.5,12)

O'(3,24)

A dilation involves the multiplication of the coordinates of each vertex of the figure by a determned scale factor k.

P → P'

(x,y) (xk, yk)

So to determine the scale factor used you have to divide the coordinates of a dilated point by the coordinates of the corresponding original point, for example for M' and M, you have to compare the corresponding coordinates, that is

x-coordinate of M' and the x-coordinate of M

-or-

y-coordinate of M' and the y-coordinate of M

`k=(x_(M^(\prime)))/(x_M)=-(10.5)/(-7)=1.5`

-or-

`k=(y_(M^(\prime)))/(y_M)=(4.5)/(3)=1.5`

The scale factor is k=1.5

The algebraic description of the transformation is:

MNO(x,y)→M'N'O'(1.5x,1.5y)