1) reflect across x=-4 essentially calculate the difference between the x=-4 line and Px and "add" it in the other direction to x=-4 A(-4-(3-(-4)),0)=A(-11,0) B(-4-(1-(-4)),-2)=B(-9,-2) C(-4-(3-(-4),-5))=C(11,-5) D(-4-(7-(-4)),-1)=D(-15,-1)
3) clockwise 90° rotation around (0,0), flip the x&y coordinates and then decide the signs they should have based on the quadrant they should be in A(0,-3) B(-2,-1) C(-5,-3) D(-1,-7)
D) Dilation at (0,0) with scale 2/3, essentially multiply all coordinates with the scale, the simple case of dilation, because the center point is at the origin (0,0) A((2/3)*3,(2/3)*0)=A(2,0) B((2/3)*1,(2/3)*-2)=B(2/3,-4/3) C((2/3)*3,(2/3)*-5)=C(2,-10/3) D((2/3)*7,(2/3)*-1)=D(14/3,-2/3)
The rectangle enclosing the path has sides of length 9 m and 14 m, so its perimeter is 2(9+14) = 46 m. The distance covered will be shorter than that.
The distance from A to C is longer than the distance from D to C, so we know the distance will be longer than 2·14+9 = 37 m.
Only one answer choice fits in the range 37 < d < 46.
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— Detailed calculation
The distance from B to C is the hypotenuse of a right triangle with sides 9 and 12. You will recognize that these side lengths are 3 times the side lengths of a 3-4-5 right triangle, so the hypotenuse distance is 3·5 = 15 meters.
