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RD Chapter 14 Co ordinate Geometry Ex 14.5 Solutions

Question - 21 : - The area of a triangle is 5 sq. units. Two of its vertices are at (2, 1) and (3, -2). If the third vertex is (7/2 , y), find y. [CBSE 2017]

Answer - 21 : -


Question - 22 : - Prove that the points (a, 0), (0, b) and (1, 1) are collinear if, 1/a + 1/b = 1.

Answer - 22 : - Let the points are A (a, 0), B (0, b) and C (1, 1) which form a triangle

Question - 23 : - The point A divides the join of P (-5, 1) and Q (3, 5) in the ratio k : 1. Find the two values of k for which the area of ∆ABC where B is (1, 5) and C (7, -2) is equal to 2 units.

Answer - 23 : - Let the coordinates of A be (x, y) which divides the join of P (-5, 1) and Q (3, 5) in the ratio. Then

Question - 24 : - The area of a triangle is 5. Two of its vertices are (2, 1) and (3, -2). The third vertex lies on y = x + 3. Find the third vertex.

Answer - 24 : - Let the coordinates of third vertex of the triangle be (x, y) and other two vertices are (2, 1) and (3, 2)

Question - 25 : - If a ≠ b ≠ c, prove that the points (a, a²), (b, b²), (c, c²) can never be collinear.

Answer - 25 : -


Question - 26 : - Four points A (6, 3), B (-3, 5), C (4, -2) and D (x, 3x) are given in such a way that △DBC/△ABC=1/2 , find x?

Answer - 26 : -

Let A (6, 3), B (-3, 5), C (4, -2) and D (x, 3x) are the vertices of quadrilateral ABCD
AC and BD are joined

Question - 27 : - If three points (x1, y1), (x2, y2), (x3, y3) lie on the same line, prove that

Answer - 27 : - Let the points (x1, y1),(x2, y2), (x3, y3)are the vertices of a triangle

Question - 28 : - Find the area of a parallelogram ABCD if three of its vertices are A (2, 4), B (2 + √3, 5) and C (2, 6). [CBSE 2013]

Answer - 28 : -

Three vertices of a ||gm ABCD are A (2, 4), B (2 + √3 , 5) and C (2, 6).
Draw one diagonal AC of ||gm ABCD

Question - 29 : - Find the value (s) of k for which the points (3k – 1, k – 2), (k, k – 7) and (k – 1, -k – 2) are collinear. [CBSE 2014]

Answer - 29 : -


Question - 30 : - If the points A (-1, -4), B (b, c) and C (5, -1) are collinear and 2b + c = 4, find the values of b and c. [CBSE 2014]

Answer - 30 : -


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