Note: This is the Solution of review exercise 7.2 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 7.2
Question # 01: Find the slope and inclination of the line joining the points:
\((i)\) \(\quad\) \((-2,4)\) ; \((5,11)\)
\((ii)\) \(\quad\) \((3,-2)\) ; \((2,7)\)
\((iii)\) \(\quad\) \((4,6)\) ; \((4,8)\)
Question 2: By means of slopes, show that the following points lie on the same line:
\((i)\) \(\quad\) \( A(-1,-3)\) ; \(B(1,5)\) ; \(C(2,9)\)
\((ii)\) \(\quad\) \( A(4,-5)\) ; \(B(7,5)\) ; \(C(10,15)\)
\((iii)\) \(\quad\) \( A(-4,6)\) ; \(B(3,8)\) ; \(C(10,10)\)
\((iv)\) \(\quad\) \( A(a,2b)\) ; \(B(c,a+b)\) ; \(C(2c-a,2a)\)
Question 3: Find \(\small{k}\) so that the line joining \(\small{A(7,3)}\) ; \(\small{B(k,-6)}\) and the line joining \(\small{C(-4,5)}\) ; \(\small{D(-6,4)}\) are:
\((i)\) \(\quad\) parallel
\((ii)\) \(\quad\) perpendicular
Question 4: Using slopes, show that the triangle with its vertices \(\small{A(6,1)}\), \(\small{B(2,7)}\) and \(\small{C(-6,-7)}\) is a right triangle.
Question 5: Two pairs of points are given. Find whether the two lines determined by these points are:
\((i)\) \(\quad\) parallel
\((ii)\) \(\quad\) perpendicular
\((ii)\) \(\quad\) none
\((a)\) \(\quad\) \((1,-2)\), \((2,4)\) and \((4,1)\), \((-8,2)\)
\((b)\) \(\quad\) \((-3,4)\), \((6,2)\) and \((4,5)\), \((-2,-7)\)
Question 6: Find an equation of:
\((a)\) \(\;\) the horizontal line through \((7, -9)\)
\((b)\) \(\;\) the vertical line through \((-5, 3)\)
\((c)\) \(\;\) through \((-6, 5)\) having slope \(7\)
\((d)\) \(\;\) through \((8, -3)\) having slope \(0\)
\((e)\) \(\;\) through \((-8, 5)\) having slope undefined
\((f)\) \(\;\) through \((-5, -3)\) and \((9,-1)\)
\((g)\) \(\;\) y-intercept: \(-7\) and slope: \(-5\)
\((h)\) \(\;\) x-intercept: \(-3\) and y-intercept: \(4\)
\((i)\) \(\;\) x-intercept: \(-9\) and slope: \(-4\)
Question 7: Find an equation of the perpendicular bisector of the segment joining the points \(\small{A(3, 5)}\), and \(\small{B(9,8)}\).
Question 8: Find an equation of the line through \(\small{(-4, -6)}\), and perpendicular to a line having slope \(\frac{-3}{2}\).
Question 9: Find an equation of the line through \(\small{(11, -5)}\), and parallel to a line with slope \(\small{-24}\).
Question 10: Convert each of the following equations into slope intercept form, two intercept form and normal form:
\((a)\) \(\quad\) \(2x-4y+11=0\)
\((ii)\) \(\quad\) \(4x+7y-2=0\)
\((iii)\) \(\quad\) \(15y-8x+3=0\)
Question 11: In each of the following check whether the two lines are:
\((i)\) \(\quad\) parallel
\((ii)\) \(\quad\) perpendicular
\((ii)\) \(\quad\) neither parallel nor perpendicular
\((a)\) \(\quad\) \(2x+y-3=0\) ; \(4x+2y+5=0\)
\((b)\) \(\quad\) \(3y=2x+5\) ; \(3x+2y-8=0\)
\((c)\) \(\quad\) \(4y+2x-1=0\) ; \(x-2y-7=0\)