The coordinates of the vertices of parallelogram rmbs are r(–4, 5), m(1, 4), b(2, –1), and s(–3, 0). using the diagonals, prove that rmbs is a rhombus. show all your work and state appropriate formulas and theorems used.

To prove a rhombus you need to show that the sides are congruent and the diagonals are perpendicular.

Sides:

≅ ≅ ≅

Diagonals:

Use the slope formula:

       = -1

       = 1

Slopes are opposite reciprocals so they are perpendicular.

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All of the sides are congruent and the diagonals are perpendicular so RMBS is a rhombus.

its an acute right triangle

step-by-step explanation:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.