need help very quickly please! thank you!

Question

Question 1: Which of the following represents a rotation of △XYZ, which has vertices X(−4,7), Y(6,2), and Z(3,−8), about the origin by 90°?

A.) X (7, −4)

     Y (−2, 6)

     Z (3, −8)

B.) X (−7, −4)

     Y (−2, 6)

     Z (8, 3)

C.) X (7, −4)

     Y (−2, 6)

     Z (−3, 8)

D.) X (−7, −4)

     Y (6, −2)

     Z (−8, 3)

Question 2: Identify the value of x and the length of each secant segment.

A.) x = 10.5; NL = 15.5; NP = 20

B.) x = 10.5; NL = 20; NP = 15.5

C.) x = 7; NL = 12; NP = 20

D.) x = 12; NL = 20; NP = 17

Please give explanation and answer please!

Answer 1

Hi Wasabi. For #1 The answer is 2. When you are rotating about the origin by 90 degrees, (x,y) becomes (-y,x)

For #2, the rule for 2 intersecting secants is a whole secant x its external part= the other whole secant x its external part.

Therefore, 20x3=(x+5)5

This gives you 60=5x+25, and then 35= 5x, so x=7

So the answer is C.