Question

1. explain the steps to use coordinates in

Answer 1

1. Use the distance formula to measure the lengths of the sides.
2. Use the slope to check whether the sides are perpendicular and form right angles.
3. Use the slope to check whether the diagonals are perpendicular to each
   

We need to explain the steps to use coordinates in calculating the perimeter and area of the polygon.

We need to explain the procedure when working with diagonal sides and irregular shapes on the coordinate plane.

The location of a point in the XY-plane is determined by coordinates. The vertex, which is the point where two lines of a shape meet to form a corner, is a unique place. We can determine the perimeter and area of a figure after we have the coordinates for all of its vertices.

Steps to calculate the perimeter and area of a polygon:

Step 1: Plot the given points on the graph.

Step 2: Connect the points and identify the figure.

Step 3: Determine lengths by counting the grid lines.

Step 4: Use a formula to calculate the perimeter and area if one exists.

Step 5: If there are no formulas for a figure, the perimeter can be calculated by summing the lengths of the sides. We might estimate the area without an area formula by counting the number of small squares enclosed.

Note: If you are using diagonal to calculate the area, then use the distance formula to calculate the length of the diagonal.

We need to explain how the distance formula and slope formula

are used to classify various quadrilaterals and triangles.

Distance formula: $\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }$

1. The length of a triangle's sides can be calculated using the distance formula.
2. If the lengths of all three sides are equal, the triangle is said to be equilateral.
3. An isosceles triangle is formed when the lengths of any two sides are equal.
4. If the length of the opposite sides is equal, then the quadrilateral could be a rectangle or a parallelogram.
5. If the length of all sides is equal, then the quadrilateral could be a square or a rhombus.

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, form right angle between them.
2. If the slope of two lines is equal, then the lines are parallel.
3. So, this gives us that the option 'Use the slope to check whether sides are perpendicular and form right angles' is correct.
4. Since some quadrilaterals have the property that the diagonals are perpendicular bisectors of each other

1. Use the distance formula to measure the lengths of the sides.
2. Use the slope to check whether the sides are perpendicular and form right angles.
3. Use the slope to check whether the diagonals are perpendicular to each

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