need help very quickly please! thank you!

Question

Question 1: Identify the translation of the figure with the vertices L(1,−1), M(4,−3), and N(3,−5), along the vector ⟨2,5⟩.

A.) L ′(3, 4), M ′(6, 2), N ′(5, 0)

B.) L ′(1, 3), M ′(6, 2), N ′(0, 5)

C.) L ′(3, 4), M ′(2, 6), N ′(5, 0)

D.) N ′(3, 4), M ′(6, 2), N ′(5, −1)

Question 2: Identify the value of x.

A.) x = 15

B.) x = 12

C.) x = 5

D.) x = 12.5

Please give explanation and answer!

Answer 1

Vector is <2, 5>

So add all the x coordinate by 2 and all the y coordinates by 3

A.) L ′(3, 4), M ′(6, 2), N ′(5, 0)

Tangent and Secant formula is AB² = BC * BD

x² = 9 * (9 + 16)

Solve for x