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The axis of symmetry of a two-dimensional figure is a line such that, if a perpendicular is constructed, any two points lying on the perpendicular at equal distances from the axis of symmetry are identical. Another way to think about it is that if the shape were to be folded in half over the axis, the two halves would be identical as mirror ...
The same reciprocal relation exists between a point P outside the circle and the secant line joining its two points of tangency. If a point P is exterior to a circle with center O, and if the tangent lines from P touch the circle at points T and S, then ∠TPS and ∠TOS are supplementary (sum to 180°).
Let the perpendicular to the line of symmetry, through the focus, intersect the parabola at a point T. Then (1) the distance from F to T is 2f, and (2) a tangent to the parabola at point T intersects the line of symmetry at a 45° angle. [13]: 26 Perpendicular tangents intersect on the directrix
An object has reflectional symmetry (line or mirror symmetry) if there is a line (or in 3D a plane) going through it which divides it into two pieces that are mirror images of each other. [6] An object has rotational symmetry if the object can be rotated about a fixed point (or in 3D about a line) without changing the overall shape. [7]
Draw a line through two points; Draw a circle through a point with a given center; Find the intersection point of two lines; Find the intersection points of two circles; Find the intersection points of a line and a circle; The initial elements in a geometric construction are called the "givens", such as a given point, a given line or a given ...
Equivalently, a line segment is the convex hull of two points. Thus, the line segment can be expressed as a convex combination of the segment's two end points. In geometry, one might define point B to be between two other points A and C, if the distance | AB | added to the distance | BC | is equal to the distance | AC |.
Let (m, n) be the point of intersection of the line ax + by + c = 0 and the line perpendicular to it which passes through the point (x 0, y 0). The line through these two points is perpendicular to the original line, so =.
The intersection point above is for the infinitely long lines defined by the points, rather than the line segments between the points, and can produce an intersection point not contained in either of the two line segments. In order to find the position of the intersection in respect to the line segments, we can define lines L 1 and L 2 in terms ...