Class 10 Exam  >  Class 10 Questions  >  Find the area of the triangle formed by joini... Start Learning for Free
Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle. Solution:?
Most Upvoted Answer
Find the area of the triangle formed by joining the mid-points of the ...
Given: The vertices of a triangle are (0, -1), (2, 1), and (0, 3).

To find: The area of the triangle formed by joining the mid-points of the sides of the given triangle and the ratio of this area to the area of the given triangle.

Solution:

Step 1: Find the mid-points of the sides of the given triangle.

The mid-point of the line segment joining the points (x1, y1) and (x2, y2) is given by:

((x1 + x2)/2, (y1 + y2)/2)

Using this formula, we can find the mid-points of the sides of the given triangle:

Mid-point of AB: ((0 + 2)/2, (-1 + 1)/2) = (1, 0)

Mid-point of BC: ((2 + 0)/2, (1 + 3)/2) = (1, 2)

Mid-point of AC: ((0 + 0)/2, (-1 + 3)/2) = (0, 1)

Step 2: Join the mid-points to form a triangle.

We join the mid-points (1, 0), (1, 2), and (0, 1) to form a triangle.

Step 3: Find the area of the triangle formed by the mid-points.

We can find the area of the triangle formed by the mid-points using the formula:

Area = 1/2 * base * height

The base of the triangle is the distance between the mid-points (1, 0) and (1, 2), which is 2 units.

The height of the triangle is the distance between the mid-point (0, 1) and the line containing the base. We can find this distance using the formula for the distance between a point and a line:

Distance = |ax + by + c| / sqrt(a^2 + b^2)

where the line is ax + by + c = 0.

The equation of the line containing the base is x = 1. Substituting this into the formula, we get:

Distance = |1(0) + 1(1) - 1| / sqrt(1^2 + 1^2) = 1 / sqrt(2)

Therefore, the height of the triangle is 1 / sqrt(2) units.

Hence, the area of the triangle formed by the mid-points is:

Area = 1/2 * base * height = 1/2 * 2 * 1/sqrt(2) = sqrt(2)

Step 4: Find the area of the given triangle.

We can find the area of the given triangle using the formula:

Area = 1/2 * base * height

where the base is the distance between any two vertices, and the height is the perpendicular distance from the third vertex to the line containing the base.

Let's take AB as the base. The distance between A(0, -1) and B(2, 1) is:

sqrt((2 - 0)^2 + (1 - (-1))^2) = sqrt(20)

The perpendicular distance from C(0, 3) to
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
Explore Courses for Class 10 exam

Top Courses for Class 10

Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle. Solution:?
Question Description
Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle. Solution:? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle. Solution:? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle. Solution:?.
Solutions for Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle. Solution:? in English & in Hindi are available as part of our courses for Class 10. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle. Solution:? defined & explained in the simplest way possible. Besides giving the explanation of Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle. Solution:?, a detailed solution for Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle. Solution:? has been provided alongside types of Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle. Solution:? theory, EduRev gives you an ample number of questions to practice Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle. Solution:? tests, examples and also practice Class 10 tests.
Explore Courses for Class 10 exam

Top Courses for Class 10

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev