Chapter 9.1, Problem 3CE

To determine

To write a program which finds whether the three given points are collinear or not. If they are not collinear find the perimeter of triangle formed by these points.

Explanation of Solution

Given:

The points A, B and C would be collinear if $\left|AB-(BC+AC)\right|,\left|AC-(BC+AB)\right|$ or $\left|BC-(AC+AB)\right|$ .

Calculation:

The following is the required BASICProgram-

10 INPUT “Enter the x-coordinate of first point”: $x_1$

20 INPUT “Enter the y-coordinate of first point”: $y_1$

30 INPUT “Enter the x-coordinate of second point”: $x_2$

40 INPUT “Enter the y-coordinate of second point”: $y_2$

40 INPUT “Enter the x-coordinate of third point”: $x_3$

50 INPUT “Enter the y-coordinate of third point”: $y_3$

60LET $AB=sqrt((x_1-x_2)\times (x_1-x_2)+(y_1-y_2)\times (y_1-y_2))$

70 LET $BC=sqrt((x_2-x_3)\times (x_2-x_3)+(y_2-y_3)\times (y_2-y_3))$

80 LET $AC=sqrt((x_1-x_3)\times (x_1-x_3)+(y_1-y_3)\times (y_1-y_3))$

90 IF $abs(AB-(BC+AC))ORabs(AC-(BC+AB))ORabs(BC-(AC+AB))$ then

100 PRINT “The points are Collinear”:

110 ELSE

120  LET $P=AB+BC+AC$

130   PRINT “The perimeter of triangle is”: $P$

140 END.

DRY RUN of the program:-

INPUT:

Enter the x-coordinate of first point

  $x_1=2$

Enter the y-coordinate of first point

  $y_1=4$

Enter the x-coordinate of second point

  $x_2=4$

Enter the y-coordinate of second point

  $y_2=6$

Enter the x-coordinate of third point

  $x_3=6$

Enter the y-coordinate of third point

  $y_3=8$

OUTPUT:

The points are Collinear.