Advertisements
Advertisements
प्रश्न
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)
Advertisements
उत्तर
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
संबंधित प्रश्न
Which point on the y-axis is equidistant from (2, 3) and (−4, 1)?
If the point P (2,2) is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.
Show that the following points are the vertices of a rectangle.
A (2, -2), B(14,10), C(11,13) and D(-1,1)
Find the ratio in which the point (-1, y) lying on the line segment joining points A(-3, 10) and (6, -8) divides it. Also, find the value of y.
Find the area of a quadrilateral ABCD whose vertices area A(3, -1), B(9, -5) C(14, 0) and D(9, 19).
Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6),R(2, -3) and S(1,2).
In what ratio does the point C (4,5) divides the join of A (2,3) and B (7,8) ?
Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?
Prove hat the points A (2, 3) B(−2,2) C(−1,−2), and D(3, −1) are the vertices of a square ABCD.
Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles.
If P ( 9a -2 , - b) divides the line segment joining A (3a + 1 , - 3 ) and B (8a, 5) in the ratio 3 : 1 , find the values of a and b .
ABCD is a parallelogram with vertices \[A ( x_1 , y_1 ), B \left( x_2 , y_2 \right), C ( x_3 , y_3 )\] . Find the coordinates of the fourth vertex D in terms of \[x_1 , x_2 , x_3 , y_1 , y_2 \text{ and } y_3\]
If the distance between points (x, 0) and (0, 3) is 5, what are the values of x?
If the distance between the points (4, p) and (1, 0) is 5, then p is equal to ______.
If (−1, 2), (2, −1) and (3, 1) are any three vertices of a parallelogram, then
If the centroid of the triangle formed by (7, x) (y, −6) and (9, 10) is at (6, 3), then (x, y) =
What is the form of co-ordinates of a point on the X-axis?
Signs of the abscissa and ordinate of a point in the second quadrant are respectively.
Point (–10, 0) lies ______.
Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So, he started to sketch his own rocket designs on the graph sheet. One such design is given below :
Based on the above, answer the following questions:
i. Find the mid-point of the segment joining F and G. (1)
ii. a. What is the distance between the points A and C? (2)
OR
b. Find the coordinates of the points which divides the line segment joining the points A and B in the ratio 1 : 3 internally. (2)
iii. What are the coordinates of the point D? (1)
