Advertisements
Advertisements
प्रश्न
If the vertices of ΔABC be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p
If the vertices of a triangle are (1, −3), (4, p) and (−9, 7) and its area is 15 sq. units, find the value(s) of p?
Advertisements
उत्तर
`Let A(x_1,y_1)= A (1,-3),B(x_2,y_2)=B(4,P) and C (x_3,y_3)= C(-9,7) Now`
`"Area" (ΔABC) = 1/2[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]`
`⇒15=1/2 [1(p-7)+4(7+3)-9(-3-p)]`
`⇒15=1/2[10p+60]`
`⇒ |10p +60|=30`
Therefore
⇒ 10p + 60 = -30 or 30
⇒ 10p = -90 or -30
⇒ p = -9 or -3
Hence , p= -9 or p= -3.
APPEARS IN
संबंधित प्रश्न
If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides
In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21/5)?
Show that the points A(6,1), B(8,2), C(9,4) and D(7,3) are the vertices of a rhombus. Find its area.
Find the coordinates of the midpoints of the line segment joining
P(-11,-8) and Q(8,-2)
In what ratio is the line segment joining A(2, -3) and B(5, 6) divide by the x-axis? Also, find the coordinates of the pint of division.
In what ratio does y-axis divide the line segment joining the points (-4, 7) and (3, -7)?
Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?
Show that `square` ABCD formed by the vertices A(-4,-7), B(-1,2), C(8,5) and D(5,-4) is a rhombus.
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is
The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b)
If points (t, 2t), (−2, 6) and (3, 1) are collinear, then t =
The distance of the point (4, 7) from the x-axis is
If point P is midpoint of segment joining point A(– 4, 2) and point B(6, 2), then the coordinates of P are ______
If the sum of X-coordinates of the vertices of a triangle is 12 and the sum of Y-coordinates is 9, then the coordinates of centroid are ______
Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?
Point (0, –7) lies ______.
The points (–5, 2) and (2, –5) lie in the ______.
If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(–2, 3) and R(–3, –2), then the coordinates of its fourth vertex S are ______.
Assertion (A): The point (0, 4) lies on y-axis.
Reason (R): The x-coordinate of a point on y-axis is zero.
