We want to draw the image of MATH after a dilation with center O(0,0) and scale factor 5.
We are told that the vertices of the polygon are M(-3,4), A(- 6,-1), T(0,0), and H(3,2). Let's start by drawing MATH on a coordinate plane.
A dilation by a scale factor of 5 can be written as D_5. Since the center of dilation is the origin O(0,0), we can find the image of each of the vertices of the quadrilateral by multiplying their coordinates by the scale factor 5. Let's do it!
MATH
M'A'T'H'
M(-3,4)
M'(-3* 5, 4* 5) ⇒ M'(-15,20)
A(- 6,- 1)
A'(- 6* 5, -1* 5) ⇒ A'(- 30,-5)
T(0,0)
T'(0* 5, 0* 5) ⇒ T'(0,0)
H(3,2)
H'(3* 5, 2* 5) ⇒ H'(15,10)
Finally, we will plot and connect the obtained vertices to draw D_5( MATH)= M' A' T' H'.
