Quadrilateral abcd is a rectangle. if ag = -7j + 7 and dg = 5j + 43, find bd

a. 56
b. -3
c. 14
d. 28

BD = 56

Step-by-step explanation:

Step 1: In rectangle, the diagonals are congruent and bisect each other.

So, AC = BD

⇒AG + GC = BG + GD

⇒AG + AG = GD + GD

⇒ 2AG = 2GD

⇒AG = GD

⇒ –7j + 7 = 5j + 43

⇒–7j – 5j = 43 – 7

⇒–12j = 36

⇒j = –3

Step 2: BD = 2DG

BD = 2(5j + 43)

     = 2(5 (–3) + 43)

     = 2(–15 + 43)

     = 2 × 28

     = 56

Hence, BD = 56.

if x decreases by 4 then y increases by 10

step-by-step explanation: