RD Chapter 14 Co ordinate Geometry Ex 14.3 Solutions
Question - 31 : - Show that the mid-point of the line segment joining the points (5, 7) and (3, 9) is also the mid-point of the line segment joining the points (8, 6) and (0, 10).
Answer - 31 : - Let M be the mid point of AB. Co-ordinates of the mid point of this line segment joining two points A (5, 7) and B (3, 9)
Question - 32 : - Find the distance of the point (1, 2) from the mid-point of the line segment joining the points (6, 8) and (2, 4).
Answer - 32 : -
Let M be the mid-point of the line segment joining the points (6, 8) and (2, 4)
Now co-ordinates of M will be
Question - 33 : - If A and B are (1, 4) and (5, 2) respectively, find the co-ordinates of P When AP/BP = 3/4
Answer - 33 : -
Point P divides the line segment joining the points (1, 4) and (5, 2) in the ratio of AP : PB = 3 : 4
Co-ordinates of P will be
Question - 34 : - Show that the points A (1, 0), B (5, 3), C (2, 7) and D (-2, 4) are the vertices of a parallelogram.
Answer - 34 : -
If ABCD is a parallelogram, then its diagonal
AC and BD bisect eachother at O
Let O is the mid-point of AC, then co
Question - 35 : - Determine the ratio in which the point P (m, 6) divides the join of A (-4, 3) and B (2, 8). Also find the value of m. [CBSE 2004]
Answer - 35 : - Let the ratio be r : s in which P (m, 6) divides the line segment joining the points A (-4, 3) and B (2, 8)
Question - 36 : - Determine the ratio in which the point (-6, a) divides the join of A (-3, -1) and B (-8, 9). Also find the value of a. [CBSE 2004]
Answer - 36 : - Let the point P (-6, a) divides the join of A (-3, -1) and B (-8, 9) in the ratio m : n
Question - 37 : - ABCD is a rectangle formed by joining the points A (-1, -1), B (-1, 4), C (5, 4) and D (5, -1). P, Q, R and S are the mid-points of sides AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square ? a rectangle ? or a rhombus ? Justify your answer.
Answer - 37 : - ABCD is a rectangle whose vertices are A (-1,-1), B (-1,4), C (5, 4) and D (5, -1) P, Q, R, and S are the mid-points of the sides AB, BC, CD and DA respectively and are joined PR and QS are also joined.
Question - 38 : - Points P, Q, R and S divide the line segment joining the pionts A (1, 2) and B (6, 7) in 5 equal parts. Find the coordinates of the points P, Q and R. [CBSE 2014]
Answer - 38 : - Points P, Q, R and S divides AB in 5 equal parts and let coordinates ofP, Q, R and S be
Coordinates of R are(4, 5)
Answer - 39 : -
Question - 40 : - Find the co-ordinates of the points which divide the line segment joining A (-2, 2) and B (2, 8) into four equal parts.
Answer - 40 : -
Let P, Q and R divides the line segment AB in four equal parts
Co-ordinates of A are (-2, 2) and of B are (2, 8)