please help with homework questions as soon as possible please !

Question

Question 1: Lara starts from the school, which is 5 miles west and 7 miles north of the house. She travels 20 miles south, and then 15 miles east. What is her final position? What single translation vector moves her from her starting position to her final position?

A.) (10, −13); (15, −20)

B.) (−5, 13); (10, −13)

C.) (−5, 7); (5, −2)

D.) (15, −20); (5, −7)

Question 2: Which of the following represents a rotation of △PQR, which has vertices P(−2,4), Q(−3,−9), and R(4,−2), about the origin by 180°?

A.) P (−4, −2)

Q (9, −3)

R (2, 4)

B.) P (2, −4)

Q (3, 9)

R (−4, −2)

C.) P (2, −4)

Q (−9, −3)

R (−4, −2)

D.) P (2, −4)

Q (3, 9)

R (−4, 2)

Please give explanation and the answer please!

Answer 1

#1)

west and south are negative, north and east are positive.

With her house at the origin, she starts at the school at (-5,7)

(15 miles east, 20 miles south) ==> (15,-20)

option A looks the best

she ends at (10,-13) but that is not asked for

#2)

180 degree rotation, according to my notes, means you NEGATE BOTH X and Y...

that is (a,b) ==> (-a,-b)

option D fits this description

Answer 2

1. Answer A.

2 P(−2,4), Q(−3,−9), and R(4,−2), about the origin, 180°

The easiest way to remember this translation is if you start in quadrant 1, (x,y), rotate it left (-x,y),

then down (-x,-y) that's 180°.

B.) P (2, −4)

Q (3, 9)

R (−4, −2)

Answer 3

Question 1:

I'm going to assume that her home is at the origin, (0,0).

School is 5 to the left and 7 up from her home. So she starts at the vector (-5, 7).

From school, she travels 20 down and 15 to the right. So she travels along the vector (15, -20) from (-5, 7).

Overall, she ends up 10 to the right and 13 down from her home. So she ends up at (10, -13).

Looks like answer A.

Question 2:

Such a rotation happens to multiply starting x values by -1 and starting y values by -1.

So (-2,4) becomes (2,-4), (-3,-9) becomes (3,9), and (4,-2) becomes (-4,2).

Looks like answer D.