Question

1.) How can I classify a quadrilateral?

2.) How can I classify a triangle?

3.) What do I use the distance formula for?

4.) How do I use the midpoint formula? What can I find with it?

5.) What is slope? How can I find it from a graph? How can I find it form two points?

6.) How can I use slope to determine if two lines (on a graph or from an equation) are parallel or perpendicular?

7.) What are the different equations of a line? What do the variables in each one represent?

8.) How can I write an equation of a line given a slope and a point?

a.) How can I write equations of lines that are parallel or perpendicular through a given point?

9.) How can I find the weighted average of two numbers?

10.) How can I find the area of a composite shape on a graph?

11.) How can I find the perimeter of a shape on a graph?

Answer 1

Explanation:

1.) To classify a quadrilateral, you can examine its properties, such as angles and side lengths. Common classifications include parallelograms, rectangles, squares, trapezoids, and rhombuses.

2.) To classify a triangle, you can analyze its angles and side lengths. Triangles can be categorized as scalene, isosceles, or equilateral based on side lengths, and as acute, obtuse, or right based on angle measures.

3.) The distance formula is used to find the distance between two points in a coordinate plane. It is represented as √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points.

4.) The midpoint formula determines the midpoint between two points in a coordinate plane. It is given by ((x1 + x2) / 2, (y1 + y2) / 2). You can find the midpoint of a line segment using this formula.

5.) Slope measures the steepness of a line. On a graph, it's the ratio of vertical change (rise) to horizontal change (run) between two points. From two points (x1, y1) and (x2, y2), slope (m) can be calculated as (y2 - y1) / (x2 - x1).

6.) If two lines have slopes that are the negative reciprocals of each other, they are perpendicular. If the slopes are equal, the lines are parallel. In equation form, two lines with slopes m1 and m2 are perpendicular if m1 * m2 = -1 and parallel if m1 = m2.

7.) The different equations of a line include the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. The point-slope form (y - y1 = m(x - x1)) uses a point (x1, y1) and the slope. The standard form (Ax + By = C) where A, B, and C are constants and A and B are not both zero.

8.) To write the equation of a line given a slope (m) and a point (x1, y1), you can use the point-slope form: y - y1 = m(x - x1).

a.) For lines parallel or perpendicular to a given line, use the fact that parallel lines have the same slope, and perpendicular lines have negative reciprocal slopes.

9.) To find the weighted average of two numbers, multiply each number by its corresponding weight, sum the products, and then divide by the sum of the weights.

10.) To find the area of a composite shape on a graph, divide the shape into simpler, recognizable shapes (triangles, rectangles, etc.), calculate their individual areas, and then sum them up.

11.) To find the perimeter of a shape on a graph, add up the lengths of all its sides. If it's a composite shape, break it into simpler shapes, find their perimeters, and then sum them up.

Answer 2

1.)

To classify a quadrilateral, you can use the following characteristics:

• The number of sides: A quadrilateral has 4 sides.
• The number of angles: A quadrilateral has 4 angles.
• The types of angles: A quadrilateral can have any combination of acute, obtuse, and right angles.
• The types of sides: A quadrilateral can have any combination of parallel, perpendicular, and non-parallel sides.

• The presence of diagonals: A quadrilateral can have 2 diagonals.

`\hrulefill`

2.)

To classify a triangle, you can use the following characteristics:

• The number of sides: A triangle has 3 sides.
• The number of angles: A triangle has 3 angles.
• The types of angles: The sum of the angles in a triangle is always 180 degrees.
• The types of sides: The sum of any two sides of a triangle must be greater than the third side.

`\hrulefill`

3.)

The distance formula is used to find the distance between two points in a coordinate plane.

The formula is:

`\sf d = √((x_2- x_1)^2 + (y_2- y_1)^2)`

where

`\sf (x_1, y_1) \:and\: (x_2, y_2)` are the coordinates of the two points.

`\hrulefill`

4.)

The midpoint formula is used to find the midpoint of a segment. The formula is:

`\sf (x_m, y_m) = \left(((x_1 + x_2))/(2), ((y_1 + y_2))/(2) \right)`

where
`\sf (x_m, y_m)` is the midpoint of the segment and
`\sf (x_1, y_1) \:and\: (x_2, y_2)` are the endpoints of the segment.

`\hrulefill`

5.)

Slope is a measure of the steepness of a line. It is calculated by finding the change in the y-coordinate divided by the change in the x-coordinate between two points on the line. The slope can be found from a graph by drawing a line connecting two points on the line and measuring the rise over run.

The slope can also be found from two points by using the following formula:

`\sf m = ((y_2 - y_)1))/((x_2 - x_1))`

where m is the slope and
`\sf \sf (x_1, y_1) \:and\: (x_2, y_2)`are the two points.

`\hrulefill`

6.)

Two lines are parallel if they have the same slope.

Two lines are perpendicular if the product of their slopes is equal to -1.

`\hrulefill`

7.)

There are three different equations of a line: the slope-intercept form, the point-slope form, and the standard form.

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line.

The standard form is Ax + By + C = 0, where A, B, and C are constants.

`\hrulefill`

8.)

To write an equation of a line given a slope and a point, you can use the point-slope form.

The formula is:

`\sf y - y1 = m(x - x_1)`

where m is the slope and (x1, y1) is the point.

a.)

To write equations of lines that are parallel or perpendicular through a given point, you can use the following formulas:

Parallel line:
`\sf : y - y1 = m(x - x1)`

Perpendicular line:
`\sf y - y_1 =( -1)/(m(x - x_1))`

`\hrulefill`

9.)

The weighted average of two numbers is found by multiplying each number by its corresponding weight and then adding the products together.

The formula is:

`\sf (\sum wx)/(\sum w)` where w is weight and x is number.

similarly

`\sf (w1 * a1 + w2 * a2 )/( w1 + w2)`

where w1 and w2 are the weights of the numbers a1 and a2.

`\hrulefill`

10.)

To find the area of a composite shape on a graph, you can divide the shape into smaller shapes that you know the area of and then add the areas of the smaller shapes together.

`\hrulefill`

11.)

To find the perimeter of a shape on a graph, you can add the lengths of all the sides of the shape together.