Question

write the x and y coordinate (in the second and third column, respectively) of dilation of quadrilateral ABCD with vertices A(1,1), B(2,2), C(4,1) and d(2,-1). Use a scale factor of 2

Answer 1

Answer:

The coordinates of the dillated vertices are $A'(x,y) = (2,2)$, $B'(x,y) = (4,4)$, $C'(x,y) = (8,2)$ and $D'(x,y) = (4,-2)$.

Step-by-step explanation:

From Linear Algebra, we define dilation by the following equation:

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation, dimensionless.

$P(x,y)$ - Original point, dimensionless.

$k$ - Scale factor, dimensionless.

$P'(x,y)$ - Dilated point, dimensionless.

If we know that $O(x,y) = (0, 0)$, $k = 2$, $A(x,y) = (1,1)$, $B(x,y) = (2,2)$, $C(x,y) = (4,1)$ and $D(x,y) = (2,-1)$, then the dilated points are, respectively:

Point A

$A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)]$ (2)

$A'(x,y) = (0,0) + 2\cdot [(1,1)-(0,0)]$

$A'(x,y) = (2,2)$

Point B

$B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)]$ (3)

$B'(x,y) = (0,0) + 2\cdot [(2,2)-(0,0)]$

$B'(x,y) = (4,4)$

Point C

$C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)]$

$C'(x,y) = (0,0) + 2\cdot [(4,1)-(0,0)]$

$C'(x,y) = (8,2)$

Point D

$D'(x,y) = O(x,y) + k\cdot [D(x,y)-O(x,y)]$

$D'(x,y) = (0,0) + 2\cdot [(2,-1)-(0,0)]$

$D'(x,y) = (4,-2)$

The coordinates of the dillated vertices are $A'(x,y) = (2,2)$, $B'(x,y) = (4,4)$, $C'(x,y) = (8,2)$ and $D'(x,y) = (4,-2)$.