Plot the points A (1, -1) and B (4, 5). Draw a line segment joining these points. Write the coordinates of a point on this line segment between the points A and B
Solution:
Given, the points are A(1, -1) and B(4, 5).
A line segment is drawn joining these points.
We have to write the coordinates of a point on this line segment between the points A and B.
Considering the point A(1, -1)
The x-coordinate is positive and the y-coordinate is negative
The point A lies in the fourth quadrant
Considering the point B(4, 5)
The x-coordinate is positive and the y-coordinate is positive
The point B lies in the first quadrant
On plotting the points A and B and joining them,
AB is a line segment.
Now draw perpendiculars from the x-axis to the line segment at x = 2 and x = 3
The perpendicular from x = 2 meet the line segment at P
The perpendicular from x = 3 meet the line segment at P’
Now draw perpendiculars from the y-axis to the line segment that intersects P and P’
The perpendicular from y = 1 intersects P
The perpendicular from y = 3 intersects P’
The coordinates of the point P are (2, 1)
The coordinates of the point P’ are (3, 3)
Therefore, the points P and P’ lie between the line segment A and B.
✦ Try This: On a graph paper, plot the points A(2, 3), B(6, -1) and C(0, 5). If these points are collinear, then draw the line which includes them. Write the coordinates of the points at which the line intersects the X-axis and the Y-axis.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 3
NCERT Exemplar Class 9 Maths Exercise 3.4 Problem 5(i)
Plot the points A (1, -1) and B (4, 5). Draw a line segment joining these points. Write the coordinates of a point on this line segment between the points A and B
Summary:
Plotting the points A (1, -1) and B (4, 5) and drawing a line segment joining these points, the coordinates of a point on this line segment between the points A and B are P(2, 1) or P’(3, 3)
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