Advertisements
Advertisements
Question
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
Solution
The verticals of the triangle are A(2,1) , B (4,3) and C(2,5).
`"Coordinates of midpoint of" AB = P (x_1,y_1)= ((2+4)/2,(1+3)/2) = (3,2)`
`"Coordinates of midpoint of " BC = Q(x_2,y_2) = ((4+2)/2,(3+5)/2) = (3,4)`
`"Coordinates of midpoint of" AC =R (x_3,y_3) = ((2+2)/2, (1+5)/2) = (2,3)`
Now,
`"Area of " ΔPQR =1/2 [x_2(y_2-y_3) +x_2 (y_3-y_1) +x_3 (y_1-y_2)]`
`=1/2[3(4-3)+3(3-2)+2(2-4)]`
`=1/2[3+3-4]=1` sq. unit
Hence, the area of the quadrilateral triangle is 1 sq. unit.
APPEARS IN
RELATED QUESTIONS
If (−2, 3), (4, −3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.
In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21/5)?
Find the co-ordinates of the point equidistant from three given points A(5,3), B(5, -5) and C(1,- 5).
Point A lies on the line segment PQ joining P(6, -6) and Q(-4, -1) in such a way that `(PA)/( PQ)=2/5` . If that point A also lies on the line 3x + k( y + 1 ) = 0, find the value of k.
`"Find the ratio in which the poin "p (3/4 , 5/12) " divides the line segment joining the points "A (1/2,3/2) and B (2,-5).`
Find the ratio in which the point P(m, 6) divides the join of A(-4, 3) and B(2, 8) Also, find the value of m.
The abscissa of any point on y-axis is
If R (x, y) is a point on the line segment joining the points P (a, b) and Q (b, a), then prove that x + y = a + b.
What is the area of the triangle formed by the points O (0, 0), A (6, 0) and B (0, 4)?
If points Q and reflections of point P (−3, 4) in X and Y axes respectively, what is QR?
Find the value of a so that the point (3, a) lies on the line represented by 2x − 3y + 5 = 0
If the points A (1,2) , O (0,0) and C (a,b) are collinear , then find a : b.
If points (a, 0), (0, b) and (1, 1) are collinear, then \[\frac{1}{a} + \frac{1}{b} =\]
f the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are
In Fig. 14.46, the area of ΔABC (in square units) is
If point P is midpoint of segment joining point A(– 4, 2) and point B(6, 2), then the coordinates of P are ______
Write the X-coordinate and Y-coordinate of point P(– 5, 4)
The points whose abscissa and ordinate have different signs will lie in ______.
In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?
