Question:
Let A(3, -1) j and B(1, 1) be the end points of line segment AB. Let P be the middle point of the line segment AB. Let Q be the point situated at a distance of 2 units from P on the perpendicular bisector line of AB. What are the possible coordinates of Q?
Let A(3, -1) j and B(1, 1) be the end points of line segment AB. Let P be the middle point of the line segment AB. Let Q be the point situated at a distance of 2 units from P on the perpendicular bisector line of AB. What are the possible coordinates of Q?
Options:
- a) (2, 1)
- b) (3, 1)
- c) (2, 2)
- d) (1, 3)
- a) (2, 1)
- b) (3, 1)
- c) (2, 2)
- d) (1, 3)
correct answer : b)
Explanation:
Coordinate of P = 31
2
11
2
+- +
,
= P(2, 0)
Slope of AB = 11
13
+
–
= -1
Equation of AB is
y – 1 = -1 (x – 1) Þ x + y – 2 = 0
Distance from Q(x, y)
xy+- 2
2
= 2
x + y – 2 = 2 Þ x + y = 4 …(i)
Slope of PQ = y
x- 2
Þ PQ ^ AB
\ (-1) y
x –
2 = -1 Þ y = x – 2
From (i)
x + x – 2 = 4 Þ x = 3 and y = 1
Q(3, 1)
Oswaal NDA/NA Year-wise Solved Papers
Coordinate of P = 31
2
11
2
+- +
,
= P(2, 0)
Slope of AB = 11
13
+
–
= -1
Equation of AB is
y – 1 = -1 (x – 1) Þ x + y – 2 = 0
Distance from Q(x, y)
xy+- 2
2
= 2
x + y – 2 = 2 Þ x + y = 4 …(i)
Slope of PQ = y
x- 2
Þ PQ ^ AB
\ (-1) y
x –
2 = -1 Þ y = x – 2
From (i)
x + x – 2 = 4 Þ x = 3 and y = 1
Q(3, 1)
Oswaal NDA/NA Year-wise Solved Papers