MATHEMATICS COLLEGE

Make a conjecture. How could the distance formula and slope be used to classify triangles and quadrilaterals in the coordinate plane? Check all that apply. Use the distance formula to measure the lengths of the sides. Use the slope to determine whether opposite sides are parallel. Use the slope to check whether sides are perpendicular and form right angles. Use the distance formula to compare whether opposite sides are congruent. Use the slope to check whether the diagonals are perpendicular to each other. Use the distance formula to compare whether diagonals are congruent.

Answers

Answer 1

Answer:

Answer:

1. Use the distance formula to measure the lengths of the sides.

3. Use the slope to check whether sides are perpendicular and form right angles.

5. Use the slope to check whether the diagonals are perpendicular to each.

Step-by-step explanation:

We know that, the distance formula given by

$d = \sqrt{ ({y_(2)-y_(1)}) ^(2)+({x_(2)-x_(1)}) ^(2)}$ ,

gives the length of the line joined by $(x_(1),y_(1))$ and $(x_(2),y_(2))$ .

Now, after using this formula, if:

1. The length of the opposite sides are equal, then the quadrilateral could be a rectangle or a parallelogram.

2. The length of all sides are equal, then the quadrilateral could be a square or a rhombus.

So, this gives us option 'Use the distance formula to measure the lengths of the sides' is correct.

Now, we use slope to find the angles i.e. If:

1. The product of two slopes is -1, then the lines are perpendicular and so, forms right angle between them.

2. The slope of two lines are equal, then the lines are parallel.

So, this gives us that the option 'Use the slope to check whether sides are perpendicular and form right angles' is correct.

Since, some quadrilaterals have the property that the diagonals are perpendicular bisector of each other.

So, the option 'Use the slope to check whether the diagonals are perpendicular to each other' is also correct.

Hence, option 1, 3 and 5 are correct.

Answer 2

Answer:

Using a limited selection from among the options, a quadrilateral, or

triangle can be classified into one of the eleven classes.

The correct options are;

Use the distance formula to measure the lengths of the sides

Use the slope to determine whether the sides are perpendicular and form right angles

Use the slope to check whether the diagonals are perpendicular

Reasons:

The classification of triangles are;

Right triangles; Having two legs that are perpendicular

Isosceles triangles; Having two sides equal

Equilateral triangles; Having all sides equal

Scalene triangle; Have all sides of different dimensions

Classification of quadrilaterals are;

Kite, rhombus, rectangle, parallelogram, square, trapezoid, isosceles trapezoid

Use the distance formula to measure the lengths of the sides;

The above process can be used to classify parallelograms, equilateral triangles, isosceles trapezoids, kite

The process can be used to classify all triangles

Use the slope to determine whether the sides are perpendicular and form right angles;

The above process can be used to differentiate parallelogram from squares and rectangles, kite trapezoid

The process can be used to determine if the triangle is a right triangle

Use the slope to check whether the diagonals are perpendicular;

The above process can be used to differentiate squares from rectangles, kite, and rhombus

Learn more about slope, distance formula, triangles and quadrilaterals here:

brainly.com/question/18652886

brainly.com/question/17962414

brainly.com/question/1058720

brainly.com/question/21338337

brainly.com/question/12767436

Related Questions

The parallelogram shown below has an area of 15 units^2Find the missing height.
a health food store sells seasoning blends in bulk. one blend contains 20% basil. sheila wants to add pure basil to some 20% blend to make 16 ounces of her own 30% blend. how much does she add to the 20% blend?
Choose the correct order of steps to solve the equation x/2+5=9 ? I. Multiply both sides by 2 II. Add 5 to both sides III. Divide both sides by 2 IV. Subtract 5 from both sides
Calculate the perimeter of a rectangle with a length of 17.5 cm and a width of 40 mm in cm
What is the measure of ∠M?A. 53° B. 65° C. 81° D. 98°

Find the complete time-domain solution y(t) for the rational algebraic output transform Y(s):_________

Answers

Answer:

y(t)= 11/3 e^(-t) - 5/2 e^(-2t) -1/6 e^(-4t)

Step-by-step explanation:

$Y(s)=(s+3)/((s^2+3s+2)(s+4)) + (s+3)/(s^2+3s+2) +(1)/(s^2+3s+2)$

We know that $s^2+3s+2=(s+1)(s+2)$ , so we have

$Y(s)=(s+3+(s+3)(s+4)+s+4)/((s+1)(s+2)(s+4))$

By using the method of partial fraction we have:

$Y(s)=(11)/(3(s+1)) - (5)/(2(s+2)) -(1)/(6(s+4))$

Now we have:

$y(t)=L^(-1)[Y(s)](t)$

Using linearity of inverse transform we get:

$y(t)=L^(-1)[(11)/(3(s+1))](t) -L^(-1)[(5)/(2(s+2))](t) -L^(-1)[(1)/(6(s+4))](t)$

Using the inverse transforms

$L^(-1)[c(1)/(s-a)]=ce^(at)$

we have:

$y(t)=11/3 e^(-t) - 5/2 e^(-2t) -1/6 e^(-4t)$

What is the circumference of circle p?
Express your answer in terms of pi.

Answers

C = 2 pi r, and r = 3ft, so C=2*pi*3 = 6pi ft.

Answer:

6π ft

Step-by-step explanation:

PA=3ft

Then just double it to get your answer.

Simplify the expression 7(1 +5v) =

Answers

the answer is 7 + 35v

Answer:

7 + 35v

Step-by-step explanation:

7 × 1 + 5v × 7

7 + 35v

Hope this helps and have a nice life d:

A swimming pool whose volume is 10 comma 000 gal contains water that is 0.03% chlorine. Starting at tequals0, city water containing 0.001% chlorine is pumped into the pool at a rate of 6 gal/min. The pool water flows out at the same rate. What is the percentage of chlorine in the pool after 1 hour? When will the pool water be 0.002% chlorine?