Author: admin
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Distance between a point and a line
The distance between a point and a line is defined to be the length of the perpendicular line segment connecting the point to the given line. Let (x1,y1) be the point not on the line and let (x2,y2) be the point on the line. To find the distance between the point (x1,y1) and the line…
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How to derive the equation of an ellipse
In order to derive the equation of an ellipse centered at the origin, consider an ellipse that is elongated horizontally into a rectangular coordinate system and whose center is placed at the origin. The foci are on the x-axis at (-c,0) and (c,0) and the vertices are also on the x-axis at (-a,0) and (a,0)…
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Definition and equation of a parabola
By definition, a parabola is the set of all points (x,y) in a plane that are the same distance from a fixed line and a fixed point not on the line. The fixed point is the focus and the fixed line is the directrix. Take a look at the figure below and make note of…
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Equation of a circle
The standard equation of a circle, also called the standard form, is (x – h)2 + (y – k)2 = r2. The radius of the circle is r, the center of the circle is (h , k), and (x , y) is any point on the circle. How to write the equation of a circle using the…
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Angle between two lines
Finding the angle between two lines using a formula is the goal of this lesson. When two lines intersect in a plane, their intersection forms two pairs of opposite angles called vertical angles. If the two lines are not perpendicular and have slopes m1 and m2, then you can use the following formula to find the…
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Inclination of a line
The inclination of a line or angle of inclination is the acute or obtuse angle that is formed when a nonhorizontal line intersects the x-axis. Formal definition: The inclination of a nonhorizontal line is the positive angle θ with θ less than 180 degrees and measured counterclockwise from the x-axis to the line. In the…
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Orthographic drawing
An orthographic drawing is a drawing that shows the top view, front view, and right-side view of a three-dimensional figure. We can also simply call the right-side view side view. Here is how to make an orthographic drawing of the three-dimensional figure below. Before you do the drawing, you need to clearly label or identify…
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Isometric drawing
An isometric drawing uses isometric dot paper in order to draw objects. It may not be easy to draw objects that have length, width, and height such as a box on a piece of paper. Isometric dot paper In order to draw or make objects that are three-dimensional on a piece of paper, you will…
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Order of rotational symmetry
The order of rotational symmetry of a geometric figure is the number of times you can rotate the geometric figure so that it looks exactly the same as the original figure. You only need to rotate the figure up to 360 degrees. Once you have rotated the figure 360 degrees, you are back to the…
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Line symmetry
A figure has line symmetry if it can be folded along a line so that one half of the figure is a mirror image of its other half. You can also say that the figure has reflectional symmetry. The reflection line is called the line of symmetry. A figure can have no line of symmetry,…