Find the coordinates for B, C, and D. Note line 1 must be perpendicular to line 2.

B = (-b, a)

C = (a, 0)

D = (-b, 0)

Step-by-step explanation:

Line 1(L₁) passes through the point O(0, 0) and A(a, b). Hence the equation of L₁ is:

Point C has the same x coordinate as point A. Since point C is on the origin line (y = 0 line), its y coordinate is 0.

The coordinate of C = (a, 0)

L₁ has a slope of b/a. Since L₂ is perpendicular to L₁, the product of their slope is -1. Hence slope of L₂ = -a/b

L₂ has a slope of -a/b and pass through  the origin. The equation of L₂ is:

But OD = AC

AC = b

Hence OD = AC = b

The y coordinate of D is 0. Let its x coordinate be -x. Hence D = (-x, 0)

The coordinate of D is (-b, 0)

B has the same x coordinate as D. The y coordinate of B is gotten by using L₂ equation and substituting x = -b

y = (-a/b)(-b)

y = a

Coordinate of B = (-b, a)

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: