Question

1. reflect the figure through (1, 2)

Explanation:

Step1: Identify original coordinates

Original points: $K(1,0)$, $M(2,5)$, $U(4,1)$

Step2: Use reflection formula over point $(a,b)$

For a point $(x,y)$, reflected point $(x',y')$ is given by:
$$x' = 2a - x$$
$$y' = 2b - y$$
Here, $(a,b)=(1,2)$

Step3: Calculate $K'$

Substitute $K(1,0)$:
$x' = 2(1) - 1 = 1$
$y' = 2(2) - 0 = 4$

Step4: Calculate $M'$

Substitute $M(2,5)$:
$x' = 2(1) - 2 = 0$
$y' = 2(2) - 5 = -1$

Step5: Calculate $U'$

Substitute $U(4,1)$:
$x' = 2(1) - 4 = -2$
$y' = 2(2) - 1 = 3$

Answer:

$K'(1, 4)$
$M'(0, -1)$
$U'(-2, 3)$