Question

structure a similarity transformation maps jklm to its image pqrs.
find the coordinates of point s.
the coordinates of point s are (□,□).
write a coordinate rule for the composition.
(x,y)→(□,□)

Explanation:

Step1: Identify key points

Original points: $K(-4,0)$, $Q(8,0)$

Step2: Find scale factor

Scale factor $k=\frac{8}{-4}=-2$

Step3: Find coordinates of $S$

Corresponding original point $M(-3,1)$. Apply scale factor:
$x$-coordinate: $-3\times-2=6$
$y$-coordinate: $1\times-2=-2$

Step4: Write coordinate rule

Apply scale factor to $(x,y)$: $(x,y)\to(kx, ky)=(-2x, -2y)$

Answer:

1. The coordinates of point $S$ are $(6, -2)$
2. $(x, y)\to(-2x, -2y)$