A(p, 0), B(4, 0), C(5, 6) And D(1, 4) Are The Vertices Of A Quadrilateral ABCD If  is Obtuse, The Maximum Integral Value Of p is

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Question

A(p, 0), B(4, 0), C(5, 6) and D(1, 4) are the vertices of a quadrilateral ABCD If  is obtuse, the maximum integral value of p is

Solution

Correct option is

2

             

⇒ (p – 1)2 + 42 + (5 – 1)2 + (6 – 4)2 < (p – 5)2 +(6)2

 and the maximum integral value of p is 2.

Testing

SIMILAR QUESTIONS

Q1

Let the sides of a triangle ABC are all integers with A as the origin. If (2, –1) and (3, 6) are points on the line AB and AC respectively (lines AB andAC may be extended to contain these points), and length of any two sides are primes that differ by 50. If a is least possible lengths of the third side and S is the least possible perimeter of the triangle then aS is equal to

Q2

If O is the origin and the coordinates of A and B are (51, 65) and (75, 81) respectively. then  is equal to

Q3

Vertices of a triangle are (0, 0), (41a, 37) and (–37, 41b) where a and bare the roots of the equation. 3x2 – 16x + 15 = 0. The area of the triangle is equal to

Q4

If O is the origin and An is the point with coordinates (n, n + 1) then (OA1)2 + (OA2)2 + …. + (OA7)2 is equal to

Q5

A(a + 1, a – 1), B(a2 + 1, a2 – 1) and C(a3 + 1, a3 – 1) are given points D(11, 9) is the mid-point of AB and E(41, 39) is the mid-point of BC. If F is the mid-point of AC the (BF)2 is equal to

Q6

Given two points A(–2, 0), and B(0,4),  is a point with coordinates (x, x), x ≥ 0P divides the joint A and B in the ratio 2 : 1. C and D are the mid-point of BM and MA respectively

1:- Area of the ΔAMB is minimum, if the coordinates of M are

Q7

Given two points A(-2, 0) and B(0, 4), M is a point with coordinates (xx), x  0. P divides the joint A and B in the ratio 2 : 1 . C and D are the mid-points of BM and AM respectively. Find the perimeter of the quadrilateral ABCD. Find the ratio of the areas of the triangles APM and BPM .

Q8

Given two points A(-2, 0) and B(0, 4), M is a point with coordinates (xx), x  0. P divides the joint A and B in the ratio 2 : 1 . C and D are the mid-points of BM and AM respectively. Find the perimeter of the quadrilateral ABCD.

Q9

Given two points A(-2, 0) and B(0, 4), M is a point with coordinates (xx), x  0. P divides the joint A and B in the ratio 2 : 1 . C and D are the mid-points of BM and AM respectively. Find the perimeter of the quadrilateral ABCD. Find the area of the quadrilateral ABCD in units.

Q10

The value of p for which  is obtuse and  is a right angle is