English, asked by sathvikaanthireddy, 1 day ago

Determine the area of the triangle MNO whose midpoints of the sides MN, NO and OM are P(2, -1), Q (4,2) and R(1,-4) respectively. s: A. O 54 sq units B. O 6 sq units C. O 42 sq units D. O 2 sq units​

Answers

Answered by eswaramoorthieswaran
1

this answer will help you

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Answered by Anonymous
4

Given:

Midpoints of sides of the triangle: P(2, -1), Q (4,2) and R(1,-4)

To find:

The area of triangle MNO

Solution:

The area of triangle MNO is 6 sq units. (Option B)

We can find the area by following the given steps-

We know that the area of the triangle formed by joining the midpoints of sides of a triangle is 1/4th of the area of the triangle.

So, the area of triangle PQR=1/4th of the area of triangle MNO.

We are given that the coordinates of the midpoints are P(2, -1), Q (4,2) and R(1,-4).

Using coordinate geometry, the area of a triangle=1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]

The coordinates of P= (x1, y1)= (2, -1)

The coordinates of Q= (x2, y2)= (4, 2)

The coordinates of R= (x3, y3)= (1, -4)

Now we will put the values in the formula,

Area of ΔPQR=1/2× |[2(2-(-4))+4(-4-(-1))+1(-1-2)]|

=1/2×|[2(6)+4(-3)+1(-3)]|

=1/2×|(12-12-3)|

=1/2×|(-3)|

= 3/2 sq units

We know that this area is 1/4th of the area of ΔMNO.

So, the area of triangle MNO=4×area of triangle PQR

On putting the values, we get

Area of ΔMNO=4×(3/2)

= 6 sq units

Therefore, the area of triangle MNO is 6 sq units.

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