Use the distance formula to show that the two triangles on the coordinate plane are congruent

Step-by-step explanation:

d =

A(- 5, - 2) , B( - 1, - 6) , C ( - 9, - 6)

AB = √[(- 5 + 1)² + (- 2 + 6)²] = 4√2

BC = √[(- 1 + 9)² + (- 6 + 6)²] = 8

AC = √[(- 5 + 9)² + (- 2 + 6)²] = 4√2

D(2, 2) , E(6, - 2) , F( 10, 2)

DE = √[(2 - 6)² + (2 + 2)²] = 4√2

EF = √[(6 - 10)² + (- 2 - 2)²] = 4√2

DF = √[(2 - 10)² + (2 - 2)²] = 8

ΔABC ≅ ΔEDF

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.