Jitender Gupta and Divya Malik Solutions for Exercise 1: CHAPTER EXERCISE

Draw the line $y=3$ on a graph. Now, draw the locus of the point on this graph, which moves in such a way that its distance from the given line is always equal to $3 \mathrm{units}$.

Use graph paper for this question.

Take $10$ small divisions$=1$ unit on both the axes. Plot the points$\mathrm{P}(2,2), \mathrm{Q}(6,4)$ and $\mathrm{R}(3,8)$.

Use graph paper for this question.

Take $10$ small divisions$=1$ unit on both the axes. For the points$\mathrm{P}(2,2), \mathrm{Q}(6,4)$ and $\mathrm{R}(3,8)$, construct the locus of points equidistant from $\mathrm{PQ}$ and $\mathrm{PR}$.

Take $10$ small divisions$=1$ unit on both the axes. For the points$\mathrm{P}(2,2), \mathrm{Q}(6,4)$ and $\mathrm{R}(3,8)$. Locate the point $\mathrm{A}$, such that $\mathrm{AP}=\mathrm{AQ}$ and $\mathrm{A}$ is equidistant from $\mathrm{PQ}$ and $\mathrm{PR}$.

Take $10$ small divisions$=1$ unit on both the axes. For the points$\mathrm{P}(2,2), \mathrm{Q}(6,4)$ and $\mathrm{R}(3,8)$. Locate the point $\mathrm{A}$, such that $\mathrm{AP}=\mathrm{AQ}$ and $\mathrm{A}$ is equidistant from $\mathrm{PQ}$ and $\mathrm{PR}$. Measure and record the length of $\mathrm{AP}$ (in $\mathrm{cm}$).

Using the ruler and compasses only, construct a $△\mathrm{FGO}$, such that $\mathrm{FG} = 4.5 \mathrm{cm}, \mathrm{FO} = 3 \mathrm{cm}$ and $\angle \mathrm{GFO}$= 45° . Complete the rectangle $\mathrm{EFGH},$ such that $\mathrm{O}$ is equidistant from $\mathrm{G} \mathrm{and} \mathrm{H}$.

Using only ruler and compasses, construct $\angle \mathrm{ABC}=120°$ , where $\mathrm{AB} =\mathrm{BC}= 5 \mathrm{cm}$. Mark two points $\mathrm{D}$and $\mathrm{E}$, which satisfy the condition that they are equidistant from both $\mathrm{BA} \mathrm{and} \mathrm{BC}.$ In the figure obtained join $\mathrm{AE}$ and $\mathrm{EC}$. Describe the figure $\mathrm{ABCD}$.

Construct a $\text{△ABC}$, with $\mathrm{AB}= 5.5 \mathrm{cm}, \mathrm{AC}=6 \mathrm{cm} ,\angle \mathrm{BAC}=105°$. Construct the locus of points equidistant from  $\mathrm{BA}$and $\mathrm{BC}$. Construct the locus of points equidistant from $\mathrm{B}$and $\mathrm{C}$ . Hence, mark the point which satisfies the above two loci as $\text{P}$. Measure and write the length of $\text{PC}$ in $\text{cm}$.