Note: This is the Solution of review exercise 7 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Review Exercise 7
Question # 01: Four option are given against each statement. Encircle the correct option.
\((i)\) The equation of a straight line in the slope-intercept form is written as:
\( a) \quad \) \( y=m(x+c) \)
\( b) \quad \) \( y-y_{1}=m(x-x_{1})\)
\(c) \quad \) \( y=c+mx\)
\( d) \quad \) \( ax+by+c=0\)
\( \text{Answer/Explanation}\)
\((ii)\) The gradient of two parallel lines are:
\( a) \quad \) equal
\( b) \quad \) zero
\(c) \quad \) negative reciprocals of each other
\( d) \quad \) always undefined
\( \text{Answer/Explanation}\)
\((iii)\) If the product of the gradients of two lines is \(-1\), then the lines are:
\( a) \quad \) Parallel
\( b) \quad \) perpendicular
\(c) \quad \) Collinear
\( d) \quad \) Coincident
\( \text{Answer/Explanation}\)
\((iv)\)\(\quad\)Distance between two points \(P(1,2)\) and \(Q(4,6)\) is:
\( a) \quad \) \(5\)
\( b) \quad \) \(6\)
\(c) \quad \) \(\sqrt{13}\)
\( d) \quad \) \(4\)
\( \text{Answer/Explanation}\)
\((v)\) \(\quad\)The midpoint of a line segment with endpoints \((-2,4)\) and \((6,-2)\) is:.
\( a) \quad \) \((4,2)\)
\( b) \quad \) \((2,1)\)
\(c) \quad \) \((1,1)\)
\( d) \quad \) \((0,0)\)
\( \text{Answer/Explanation}\)
\((vi)\) \(\quad\) A line passing through points \((1,2)\) and \((4,5)\) is:
\( a) \quad \) \(y=x+1\)
\( b) \quad \) \(y=2x+3\)
\(c) \quad \) \(y=3x-2\)
\( d) \quad \) \(y=x+2\)
\( \text{Answer/Explanation}\)
\((vii)\)\(\quad\)The equation of a line in point-slope form is:
\( a) \quad \) \(y=m(x+c)\)
\( b) \quad \) \(y-y_{1}=m(x-x_{1})\)
\(c) \quad \) \(y=c+mx\)
\( d) \quad \) \(ax+by+c=0\)
\( \text{Answer/Explanation}\)
\((viii)\)\(\quad\)\(2x+3y-6=0\) in the slope-intercept form is:
\( a) \quad \) \( y=\frac{-2}{3}x+2\)
\( b) \quad \) \( y=\frac{2}{3}x-2\)
\(c) \quad \) \( y=\frac{2}{3}x+1\)
\( d) \quad \) \( y=\frac{-2}{3}x-2\)
\( \text{Answer/Explanation}\)
\((ix)\)\(\quad\)The equation of a line in symmetric form is:
\( a) \quad \) \(\frac{x}{a}+\frac{y}{b}=1\)
\( b) \quad \) \(\frac{x-x_{1}}{1}+\frac{y-y_{1}}{m}=\frac{z-z_{1}}{1}\)
\(c) \quad \) \(ax+by+c=0\)
\( d) \quad \) \(y-y_{1}=m(x-x_{1})\)
\( \text{Answer/Explanation}\)
\((x)\) \(\quad\)The equation of a line in normal form is:
\( a) \quad \) \(y=mx+c\)
\( b) \quad \) \(\frac{x}{a}+\frac{y}{b}=1\)
\(c) \quad \) \(\frac{x-x_{1}}{\cos \alpha}=\frac{y-y_{1}}{\sin \alpha}\)
\( d) \quad \) \(x\cos \alpha +y\sin \alpha =p\)
\( \text{Answer/Explanation}\)
Question 2: Find the distance between two points \(\small{A(2,3})\) and \(\small{B(7,8)}\) on a coordinate plane.
Question 3: Find the midpoint of the line segment joining the points \(\small{A(4,-2)}\) and \(\small{B(-6,3)}\).
Question 4: Calculate the gradient (slope) of the line passing through points \(\small{A(1,2)}\) and \(\small{B(4,6)}\).
Question 5: Find the equation of the line in the form \(\small{y=mx+c)}\) that passes through the points \(\small{(3,7)}\) and \(\small{(5,11)}\).
Question 6: If two lines are parallel and one line has a gradient of \(\small{\frac{2}{3}}\), what is the gradient of the other line?
Question 7: An airplane needs to fly from city \(\small{A}\) to coordinate \(\small{(12,5)}\) to city \(\small{B}\) at coordinates \(\small{(8,-4)}\). Calculate the straight-line distance between thse two cities.
Question 8: In a landscaping project, the path starts at \(\small{(2,3)}\) and ends at \(\small{(10,7)}\). Find the midpoint.
Question 9: A drone flying from point \(\small{(2,3)}\) to point \(\small{(10,15)}\) on the grid. Calculate the gradient of the line along which the drone is flying and the total distance travelled.
Question 10: For a line with a gradient of \(\small{-3}\) and a y-intercept of \(\small{2}\), write the equation of the line in:
\((a)\) \(\quad\)Slope-intercept form
\((b)\) \(\quad\)Point-slope form using the point \((1,2)\)
\((c)\) \(\quad\)Two-point form using the points \((1,2)\) and \((4,-7)\)
\((d)\) \(\quad\)Intercepts form
\((e)\) \(\quad\)Symmetric form
\((f)\) \(\quad\)Normal form