Prove that the area of the triangle with vertices at `(p-4,p+5),(P+3,p-2) and (p,p) ` remains constant as p varies and explain the result.

P(x, y) moves such that the area of the triangle with vertices at P(x, y), (1, -2), (-1, 3) is equal to the area of the triangle with vertices at P(x, y), (2, -1), (3, 1). The locus of P is

If the area of the triangle formed by the vertices (p,p),(5,6),(5,-2) is 32 sq. units. Find the value of p.

The area of the triangle is 18 sq.units, whose vertices are (3 , 4) , (- 3 , -2) and (p , -1), then find the value of 'p' .

The area of triangle formed by the points (p, 2-2p), (1-p, 2p) and (- 4-p, 6-2p) is 70 unit. How many integral values of p are possible?

if the vertices of a triangle are (1,-3)(4,p)(-9,7) and its are area 15 Squnits then find the value of P

If P_1, P_2 and P_3 are the altitudes of a triangle from vertices A, B and C respectively and Delta is the area of the triangle, then the value of 1/P_1+1/P_2-1/P_3=

If p_1,p_2,p_3 are altitudes of a triangle ABC from the vertices A,B,C respectively and Delta is the area of the triangle and s is semi perimeter of the triangle. If 1/p_1+1/p_2+1/p_3=1/2, then the least value of p_1p_2p_3 is

If p_1,p_2,p_3 are altitudes of a triangle ABC from the vertices A,B,C respectively and Delta is the area of the triangle and s is semi perimeter of the triangle The value of cosA/p_1+cosB/p_2+cosC/p_3 is

p_1,p_2,p_3 are the altitudes of a triangle ABC drawn from the vertices A,B and C respictively . If Delta is the area of the triangle and 2s is the sum of its sides, a,b and c then 1/(p_1)+1/(p_2)-1/(p_3)=