A ray in geometry is like a line with a starting point but no end. It begins at one point and keeps going forever in one direction. The point where the ray begins is called the endpoint, and from there, it extends endlessly. If AB is a ray, it is denoted as
Two lines are referred to as perpendicular if they intersect at a right angle (90 degrees). This relation is represented in diagrams with a small square at the intersection point, indicating the right angle. It is mathematically represented by the symbol ⟂. If two lines p and q are perpendicular it is written as p ⟂ q.
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Steps to Draw a Perpendicular from the Endpoint of Ray
Drawing a perpendicular from the endpoint of a ray requires a compass, ruler, and pencil. We can draw a perpendicular from the endpoint by using two methods: by using the diameter of the circle and by extending the ray endpoint.
Method 1: By Diameter of Circle
The steps to construct a perpendicular from the endpoint of a ray by the diameter of a circle are as follows.
- Step 1: First identify the endpoint A of the ray.
- Step 2: Now, mark a point P above the ray so that the point P is approx. 6cm away from point A.
- Step 3: Now, take a compass and measure the length between points A and P, then by taking P as the center draw an arc intersecting the endpoint of the ray and ray and mark the intersection point as C.
- Step 4: Now, take a ruler and draw a straight line connecting points C, P and arc.
- Step 5: Mark the point intersecting the arc as D.
- Step 6: Now, draw a straight line connecting points A and D that represents the perpendicular from the endpoint of the ray.
Here, AD is the perpendicular from the endpoint of the ray AB.
Method 2: Extend the ray by its endpoint
The steps to construct a perpendicular from endpoint of a ray by extending ray are as follows.
Step 1: First, we have to identify the ray and its endpoint. Let
\overrightarrow{\rm AB} be a ray and A be its endpoint.Step 2: Now, extend the ray in opposite side of the endpoint and mark A as the point to construct perpendicular.
Step 3: Now, take a compass and put it at point A and draw arcs intersecting the ray at two points C and D.
Step 4: Now measure the length between point C and D with compass draw arcs above and below the ray with point C as center and further point D as center.
Step 5: Name the arcs intersection points as P and Q.
Step 6: Use a ruler and draw straight line joining point P and Q.
The Line PQ represents the perpendicular from the endpoint A of the ray
Applications of Perpendiculars from a Ray's Endpoint
Some applications of perpendiculars from a ray's endpoint are as follows:
- The perpendicular from ray's endpoint is used in construction of the buildings to provide correct angles and for perpendicular columns and beams and structure design to provide it stability.
- It is also used in engineering in different fields like circuit design, computer graphics, animation, robotics, automation etc.
- It is also used in mathematics in fields like vector calculus and many more.
- It is also used in designing arts to draw different perspectives and illusions.
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