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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.

Respuesta :

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

[tex]d = \sqrt{ ({y_{2}-y_{1}}) ^{2}+({x_{2}-x_{1}}) ^{2}}[/tex],

gives the length of the line joined by [tex](x_{1},y_{1})[/tex] and  [tex](x_{2},y_{2})[/tex].

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.

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

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