Question

Read the graph and write the answer of the following questions.
figure

(i) Write the co-ordinates of the points A, B, C, D, E, F, Q, P and H
(ii) Which co-ordinate of point B is zero?
(iii) Which points have co-ordinates ($-$1, $-$5) and (3, 2)?
(iv) To which axis the line AH is parallel?
(v) Which co-ordinate of point P and Q is the same?
(vi) Which co-ordinate of E is 3?
(vii) To which axis the line EQ is parallel?
(viii) M is any point on the line AH, then state its x-co-ordinate.

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{C}o-\mathrm{ordinates}\mathrm{of}\mathrm{the}\mathrm{points}\mathrm{are}: \\ \mathrm{A}\equiv \left(3,2\right) \\ \mathrm{B}\equiv \left(5,0\right) \\ \mathrm{C}\equiv \left(-5,6\right) \\ \mathrm{D}\equiv \left(-3,0\right) \\ \mathrm{E}\equiv \left(-6,3\right) \\ \mathrm{F}\equiv \left(-1,-5\right) \\ \mathrm{Q}\equiv \left(7,3\right) \\ \mathrm{P}\equiv \left(7,-2\right) \\ \mathrm{H}\equiv \left(3,-4\right) \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right)\mathrm{B}\equiv \left(5,0\right) \\ \therefore \mathrm{y}-\mathrm{coordinate}\mathrm{of}\mathrm{point}\mathrm{B}\mathrm{is}\mathrm{zero}. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right)\mathrm{Point}\mathrm{F}\mathrm{has}\mathrm{coordinate}\text{s}\left(-1,-5\right) \\ \mathrm{and}\mathrm{Point}\mathrm{A}\mathrm{has}\mathrm{coordinate}\text{s}\left(3,2\right). \end{gathered}$$

$\left(\mathrm{iv}\right)\mathrm{Line}\mathrm{AH}\mathrm{is}\mathrm{parallel}\mathrm{to}\mathrm{Y}-\mathrm{axis}.$

$$\begin{gathered} \left(\mathrm{v}\right)\mathrm{Coordinate}\text{s}\mathrm{of}\mathrm{point}\mathrm{P}\equiv \left(7,-2\right) \\ \mathrm{and}\mathrm{coordinate}\text{s}\mathrm{of}\mathrm{point}\mathrm{Q}\equiv \left(7,3\right). \\ \mathrm{Therefore},\mathrm{x}-\mathrm{coordinate}\mathrm{of}\mathrm{point}\text{s}\mathrm{P}\mathrm{and}\mathrm{Q}\mathrm{are}\mathrm{same}. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{vi}\right)\mathrm{E}\equiv \left(-6,3\right) \\ \therefore \mathrm{y}-\mathrm{coordinate}\mathrm{of}\mathrm{point}\mathrm{E}\mathrm{is}3. \end{gathered}$$

$\left(\mathrm{vii}\right)\mathrm{Line}\mathrm{EQ}\mathrm{is}\mathrm{parallel}\mathrm{to}\mathrm{X}-\mathrm{axis}.$

$$\begin{gathered} \left(\mathrm{viii}\right)\mathrm{Line}\mathrm{AH}\mathrm{is}\mathrm{parallel}\mathrm{to}\mathrm{Y}-\mathrm{axis}. \\ \mathrm{Therefore},\mathrm{on}\mathrm{every}\mathrm{point}\mathrm{on}\mathrm{this}\mathrm{line},\text{the}\mathrm{x}-\mathrm{coordinate}\mathrm{will}\mathrm{be}\mathrm{equal}\mathrm{to}3. \\ \mathrm{Therefore},\mathrm{x}-\mathrm{coordinate}\mathrm{of}\mathrm{point}\mathrm{M}\mathrm{will}\mathrm{be}3. \end{gathered}$$