Note: This is the Solution of review exercise 7.1 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 7.1
Question # 01: Describe the location in the plane of the point \(\small{P(x,y)}\), for which
\((i)\) \(\quad\) \( x>0\)
\((ii)\) \(\quad\) \(x>0\) and \(y>0\)
\((iii)\) \(\quad\) \(x=0 \)
\((iv)\) \(\quad \)\(y=0 \)
\((v)\) \(\quad \) \(x\ge 0 \) and \(y<0\)
\((vi)\) \(\quad \) \(y=0 \) , \(x=0\)
\((vii)\) \(\quad \) \(|x|=|y| \)
\((viii)\) \(\quad \) \(x\ge 3 \)
\((ix)\) \(\quad \) \(y>2 \)
\((x)\) \(\quad \) \(x\) and \(y\) have opposite signs.
Question 2: Find the distance between the points:
\((i)\) \(\quad\) \( A(6,7)\),\(B(0,-2)\)
\((ii)\) \(\quad\) \( C(-5,-2)\),\(D(3,2)\)
\((iii)\) \(\quad\) \( L(0,3)\),\(M(-2,-4)\)
\((iv)\) \(\quad\) \( P(-8,-7)\),\(Q(0,0)\)
Question 3: Find in each of the following:
\((i)\) \(\quad\) The distance between the two given points
\((ii)\) \(\quad\) Midpoint of the line segment joining the two points:
\((a)\) \(\quad\) \(A(3,1)\) , \(B(-2,-4)\)
\((b)\) \(\quad\) \(A(-8,3)\) , \(B(2,-1)\)
\((c)\) \(\quad\) \(A(-\sqrt{5},-\frac{1}{3})\) , \(B(-3\sqrt{5},5)\)
Question 4: Which of the following points are at a distance of \(15\) units from the origin?
\((i)\) \(\quad\) \( (\sqrt{176},7)\)
\((ii)\) \(\quad\) \((10,-10)\)
\((iii)\) \(\quad\) \((1,15) \)
Question 5: Show that:
\((i)\) \(\;\) the points \(A(0,2)\) , \(B(\sqrt{3},1)\) and \(C(0,-2)\) are vertices of a right triangle.
\((i)\) \(\;\) the points \(A(3,1)\) , \(B(-2,-3)\) and \(C(2,2)\) are vertices of an isoceles triangle.
\((iii)\) \(\;\) the points \(A(5,2)\) , \(B(-2,3)\), \(C(-3,-4)\) and \(D(4,-5)\) are vertices of a parallelogram.