How do you find a point on a line given the equation?

To find points on the line y = mx + b,

1. choose x and solve the equation for y, or.
2. choose y and solve for x.

How do you find whether a point lies inside a triangle?

A simple way is to: find the vectors connecting the point to each of the triangle’s three vertices and sum the angles between those vectors. If the sum of the angles is 2*pi then the point is inside the triangle.

How do you find the equation of a line in a triangle?

The straight line through two points will have an equation in the form y = m x + c . We can find the value of , the gradient of the line, by forming a right-angled triangle using the coordinates of the two points.

How do you find if a point is above or below a line?

If y is the ordinate of P, then (x1,y) are the coordinates of P. Since P lies on the line (i), it must satisfy the equation of the line, i.e. Next we consider the difference y1–y, i.e. (a) If the point A is above the line, then y1–y>0.

How do you find the equation of a line when given the slope and a point?

These are the two methods to finding the equation of a line when given a point and the slope:

1. Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b.
2. Point-slope form = y − y 1 = m ( x − x 1 ) , where ( x 1 , y 1 ) is the point given and m is the slope given.

How do you know if three points form a triangle?

Approach: A triangle is valid if sum of its two sides is greater than the third side. If three sides are a, b and c, then three conditions should be met.

Which of the following points of a triangle must lie inside the triangle?

The incenter is the point of concurrency of the angle bisectors of all the interior angles of the triangle. In other words, the point where three angle bisectors of the angles of the triangle meet are known as the incenter. The incenter always lies within the triangle.

How do you find the third side of a triangle?

In this case, use The Law of Sines first to find either one of the other two angles, then use Angles of a Triangle to find the third angle, then The Law of Sines again to find the final side.

How do you find the last angle of a triangle?

This means we are given two sides and the included angle. For this type of triangle, we must use The Law of Cosines first to calculate the third side of the triangle; then we can use The Law of Sines to find one of the other two angles, and finally use Angles of a Triangle to find the last angle.

What is the formula to find the cosine of a triangle?

For a triangle with sides a, b, and c, if a and b are known and C is the included angle (the angle between the sides), C can be worked out with the cosine rule. The formula is as follows: c2 = a2 + b2 – 2ab cos C.

What does it mean to solve a triangle?

“Solving” means finding missing sides and angles. When we know any 3 of the sides or angles one side to find how big the triangle is.) If you need to solve a triangle right now choose one of the six options below: Which Sides or Angles do you know already? (Click on the image or link)