What is the area of this triangle in the coordinate plane? 5 units² 6 units² 7 units² 12 units² A graph with a triangle drawn between coordinates begin ordered pair 1 comma 1 end ordered pair begin ordered pair 1 comma 4 end ordered pair and coordinates begin ordered pair 5 comma 1 end ordered pair

6 units²

Step-by-step explanation:

The coordinates (1,1) (1,4) (5,1)  form a right triangle as shown in the graph below

The base is  is (1,1) and (5,1) so the length is 5-1 or 4 units

The height is (1,1) and (1,4) so the height is 4-1 or 3 units

Area of a triangle is given by

A = 1/2 bh

    = 1/2 (4*3)

    = 1/2 *12

    = 6 units^2

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

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: