Understand Distance formula with the help Sample numerical. Click on the Link to Watch the VIDEO explanation: Watch Video
Numerical
Prove that the points A (1, 1), B (-1, -1) and C (minus root 3, root 3) form an equilateral triangle and also find the area of the triangle.
Solution
Mark three points A (1, 1), B (-1, -1) and C (minus root 3, root 3) arbitrarily.
We need to first calculate the distance between these points.
So let us apply the distance formulae and calculate the distances.
Distance between the points A (one, one) and B (minus one, minus one).
AB is equal to the root of x2 minus x1 the whole square plus y2 minus y1 the whole square.
Here x1, y1 is equal to one, one and x2, y2 is equal to minus one, minus one.
Key in the values of x1, y1 and x2, y2 in the respective boxes and obtain the value of AB.
Click on the OK button to check your answer.
Else click on the Solve button to find the value of AB.
Therefore AB is equal to root eight units.
Distance between the points B (minus one, minus one) and C (minus root three, root three).
Here x1, y1 is equal to minus one, minus one and x2, y2 is equal to minus root three, root three.
Calculate distance BC.
Therefore BC is equal to root eight units.
Distance between the points C (minus root three, root three) and A (one, one).
Calculate the distance CA.
Hence CA is equal to root eight units.
Therefore AB is equal to BC is equal to CA. This is equal to root eight units.
Join AB, BC and CA.
If all the three sides of triangle are equal, then the triangle is known as an Equilateral triangle.
In triangle ABC, AB is equal to BC is equal to CA.
Therefore triangle ABC is an equilateral triangle.
Now, we need to calculate the area of triangle ABC.
We have AB is equal to BC is equal to CA. This is equal to root eight units.
Area of an equilateral triangle is equal to root three by four into side square.
Therefore, calculate the area of equilateral triangle ABC by keying in the value of side.
Therefore area of equilateral triangle ABC is equal to two root three units.
Numerical
Prove that the points A (1, 1), B (-1, -1) and C (minus root 3, root 3) form an equilateral triangle and also find the area of the triangle.
Solution
Mark three points A (1, 1), B (-1, -1) and C (minus root 3, root 3) arbitrarily.
We need to first calculate the distance between these points.
So let us apply the distance formulae and calculate the distances.
Distance between the points A (one, one) and B (minus one, minus one).
AB is equal to the root of x2 minus x1 the whole square plus y2 minus y1 the whole square.
Here x1, y1 is equal to one, one and x2, y2 is equal to minus one, minus one.
Key in the values of x1, y1 and x2, y2 in the respective boxes and obtain the value of AB.
Click on the OK button to check your answer.
Else click on the Solve button to find the value of AB.
Therefore AB is equal to root eight units.
Distance between the points B (minus one, minus one) and C (minus root three, root three).
Here x1, y1 is equal to minus one, minus one and x2, y2 is equal to minus root three, root three.
Calculate distance BC.
Therefore BC is equal to root eight units.
Distance between the points C (minus root three, root three) and A (one, one).
Calculate the distance CA.
Hence CA is equal to root eight units.
Therefore AB is equal to BC is equal to CA. This is equal to root eight units.
Join AB, BC and CA.
If all the three sides of triangle are equal, then the triangle is known as an Equilateral triangle.
In triangle ABC, AB is equal to BC is equal to CA.
Therefore triangle ABC is an equilateral triangle.
Now, we need to calculate the area of triangle ABC.
We have AB is equal to BC is equal to CA. This is equal to root eight units.
Area of an equilateral triangle is equal to root three by four into side square.
Therefore, calculate the area of equilateral triangle ABC by keying in the value of side.
Therefore area of equilateral triangle ABC is equal to two root three units.
No comments:
Post a Comment