Orienting Yourself: The Use of Coordinates

What are the standard widths for a room door? Look around your home and in school.

Are the doors in your school suitable for people in wheelchairs?

What is the x-coordinate of a point on the y-axis?

Is there a similar generalisation for a point on the x-axis?

Does point $Q\,(y,\, x)$ ever coincide with point $P\,(x,\, y)$? Justify your answer.

If x $\neq$ y, then (x, y) $\neq$ (y, x); and (x, y) = (y, x) if and only if x = y. Is this claim true?

Place Reiaan's rectangular study table with three of its feet at the points $(8, 9)$, $(11, 9)$ and $(11, 7)$.

In moving from $A\ (3,\ 4)$ to $D\ (7,\ 1)$, what distance has been covered along the x-axis? What about the distance along the y-axis?

Can these distances help you find the distance AD?

What has remained the same and what has changed with this reflection?

Would these observations be the same if $\Delta ADM$ is reflected in the $x$-axis (instead of the $y$-axis)?

What are the x-coordinate and y-coordinate of the point of intersection of the two axes?

Point $W$ has $x$-coordinate equal to $-5$. Can you predict the coordinates of point $H$ which is on the line through $W$ parallel to the $y$-axis? Which quadrants can $H$ lie in?

Consider the points $R\,(3,\,0)$, $A\,(0,\,{-2})$, $M\,(-5,\,{-2})$ and $P\,(-5,\,2)$. If they are joined in the same order, predict:

Plot point Z (5, −6) on the Cartesian plane. Construct a right-angled triangle IZN and find the lengths of the three sides.

What would a system of coordinates be like if we did not have negative numbers? Would this system allow us to locate all the points on a 2-D plane?

Are the points $M (-3, -4)$, $A (0, 0)$ and $G (6, 8)$ on the same straight line? Suggest a method to check this without plotting and joining the points.

Use your method (from Problem 6) to check if the points $R\,(-5,\,-1)$, $B\,(-2,\,-5)$ and $C\,(4,\,-12)$ are on the same straight line. Now plot both sets of points and check your answers.

Using the origin as one vertex, plot the vertices of:

Use the connection you found to find the coordinates of B given that M (−7, 1) is the midpoint of A (3, −4) and B (x, y).