Class 9th math 11.2 solution english PCTB

Question # 01: Two points \(\small{A}\) and \(\small{B}\) are \(\small{8.2\ cm}\) apart. Construct the locus of points \(\small{5\ cm}\) from point \(\small{A}\).

Question 2: Construct a locus of point \(\small{2.2\ cm}\) from line segment \(\small{CD}\) of measures \(\small{5.7\ cm}\)

Question 3: Construct an angle \(\small{ABC=105^\circ}\). Costruct a locus of a point \(\small{P}\) which moves such that it is equidistant from \(\small{\overline{BA}}\) and \(\small{\overline{BC}}\).

Question 4: Two points \(\small{E}\) and \(\small{F}\) are \(\small{5.4\ cm}\) apart. Construct a locus of a point \(\small{P}\) which moves such that it is equidistant from \(\small{E}\) and \(\small{F}\).

Question 5: The island has two main cities \(\small{A}\) and \(\small{B}\) \(\small{8\ km}\) apart. Kashif lives on the island exactly \(\small{6.8\ km}\) from city \(\small{A}\) and exactly \(\small{7.3\ km}\) from city \(\small{B}\). Mark with a cross the points on the island where Kashif could live.

Question 6: Construct a triangle \(\small{CDE}\) with \(\small{m\overline{CD}=7.6\ cm}\), \(\small{m\angle{D}=45^\circ}\) and \(\small{m\overline{DE}=5.9\ cm}\). Draw the locus of all points which are:

Mark the point \(X\) where the two loci intersect.

Question 7: Construct a triangle \(\small{LMN}\) with \(\small{m\overline{LM}=7\ cm}\), \(\small{m\angle L=70^\circ}\) and \(\small{m\angle M=45^\circ}\). Find a point within the triangle \(\small{LMN}\) which is equidistant from \(\small{L}\) and \(\small{M}\) and \(\small{3\ cm}\) from \(\small{L}\).

Question 8: Construct a right angled triangle \(\small{RST}\) with \(\small{m\overline{RS}=6.8\ cm}\), \(\small{m\angle S=90^\circ}\) and \(\small{m\overline{ST}=7.5\ cm}\). Find a point within the triangle \(\small{RST}\) which is equidistant from \(\small{\overline{RS}}\) and \(\small{\overline{RT}}\) and \(\small{4.5\ cm}\) from \(\small{R}\).

Question 9: Construct a rectangle \(\small{UVWX}\) with \(\small{m\overline{UV}=7.2\ cm}\) and \(\small{m\overline{vW}=5.6\ cm}\). Draw the locus of points at a distance of \(\small{2\ cm}\) from \(\small{\overline{UV}}\) and \(\small{3.5\ cm}\) from \(\small{W}\).

Question 10: Imagine two cell towers located at points \(\small{A}\) and \(\small{B}\) on a coordinate plane. The GPS-enabled device, positioned somewhere on the plane, recieves signals form both towers. To ensure accurate navigation, the device is placed equidistant from both towers to estimate its position. Draw this locus of navigation.

Question 11: Epidemiologists use loci to determine infection zones, especially for contagious disease, to predict the spread and take containment measures. In the case of a disease outbreak, authorities might determine a quarntine zone within \(\small{10\ km}\) of the infection source. Draw the locus of all points \(\small{10\ km}\) from the source defining the quarantine area to monitor and control the disease’s spread.

Question 12: There is a treasure buried somewhere on the island. The treasure is \(\small{24\ km}\) from \(\small{A}\) and equidistant from \(\small{B}\) and \(\small{C}\). Using a scale of \(\small{1\ cm}\) to represent \(\small{10\ km}\), find where the treasure could be buried.

Question 13: There is an apple tree at a distance of \(\small{90}\) meters from banana tree in the garden of Sara’s house. Sara wants to plant a mango tree \(\small{M}\) which is \(\small{64}\) meters from apple tree and between \(\small{54}\) and \(\small{82}\) meters from the banana tree. Using a scale of \(\small{1\ cm}\) to represent \(\small{10\ m}\), Find the points whre the mango tree should be planted.