Saved Bookmarks
| 1. |
If the vertices of a triangle ABC are(-5,2)(9-3)(-3,5)then find the area of the triangle formed by the mid points of sides of triangle ABC |
|
Answer» Step-by-step explanation: MATHS Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose VERTICES are (2,2), (4,4) and (2,6). January 17, 2020avatar Kanishka Londhe SHARE ANSWER Let A(2,2),B(4,4) and C(2,6) be the vertices of a given triangle ABC. Let D, E, and F be the midpoints of AB, BC and CA respectively. Mid point of two points (x 1
,y 1
) and (x 2
,y 2
) is CALCULATED by the formula ( 2 x 1
+x 2
, 2 y 1
+y 2
) Using this formula,the coordinates of D, E, and F are given as D( 2 2+4
, 2 2+4
),E( 2 4+2
, 2 4+6
) and F( 2 2+2
, 2 2+6
) i.e., D(3,3),E(3,5)andF(2,4) Area of a triangle with vertices (x 1
,y 1
) ; (x 2
,y 2
) and (x 3
,y 3
) is ∣ ∣ ∣ ∣ ∣
2 x 1
(y 2
−y 3
)+x 2
(y 3
−y 1
)+x 3
(y 1
−y 2
)
∣ ∣ ∣ ∣ ∣
Hence, substituting the points (x 1
,y 1
)=(3,3) ; (x 2
,y 2
)=(3,5) and (x 3
,y 3
)=(2,4) in the area formula, we get Area of triangle DEF = ∣ ∣ ∣ ∣ ∣
2 3(5−4)+(3)(4−3)+2(3−5)
∣ ∣ ∣ ∣ ∣
= ∣ ∣ ∣ ∣ ∣
2 3+3−4
∣ ∣ ∣ ∣ ∣
= 2 2
=1 SQ units |
|