Q. 215.0( 3 Votes )

# Two vertices of a triangle are (-2, -1) and (3, 2) and third vertex lies on the line x + y = 5. If the area of the triangle is 4 square units, then the third vertex is

A. (0, 5) or, (4, 1)

B. (5, 0) or, (1, 4)

C. (5, 0) or, (4, 1)

D. (0, 5) or, (1, 4)

Answer :

Let (h, k) be the third vertex of the triangle.

It is given that the area of the triangle with vertices (h, k), (− 2, − 1) and (3, 2) is 4 square units.

⇒ 3h – 5k + 1 = ± 8

Taking positive sign, we get,

3h – 5k + 1 = 8

3h – 5k – 7 = 0 … (1)

Taking negative sign, we get,

3h – 5k + 9 = 0 … (2)

The vertex (h, k) lies on the line x + y = 5.

H + k – 5 = 0 … (3)

On solving (1) and (3), we find (4, 1) to be the coordinates of the third vertex.

Similarly, on solving (2) and (3), we find (2, 3) to be the coordinates of the third vertex.

Rate this question :

The figure formed by the lines ax ± by ± c = 0 is

RD Sharma - MathematicsThe centroid of a triangle is (2, 7) and two of its vertices are (4, 80 and (-2, 6). The third vertex is

RD Sharma - MathematicsTwo vertices of a triangle are (-2, -1) and (3, 2) and third vertex lies on the line x + y = 5. If the area of the triangle is 4 square units, then the third vertex is

RD Sharma - MathematicsThree vertices of a parallelogram taken in order are (-1, -6), (2, -5) and (7, 2). The fourth vertex is

RD Sharma - MathematicsA(6, 3), B(-3, 5), C(4, -2) and (x, 3x) are four points. If ΔDBC : ΔABC = 1 : 2, then x is equal to

RD Sharma - MathematicsIf the point (5, 2) bisects the intercept of a line between the axes, then its equation is

RD Sharma - MathematicsWrite the area of the figure formed by the lines a|x| + b|y| + c = 0

RD Sharma - Mathematics