Question

topic question type question wording question 1 plotting points 5 marks type answer plot five points and state their location on the cartesian plane question 2 graphing lines 6 marks type answer graph three lines question 3 midpoint, distance, & slope 7 marks type answer calculate the midpoint and distance and slope between two points

Explanation:

Question 1:

1. Step1: Choose five points

Let the points be $(1,1)$, $( - 1,2)$, $(0, - 3)$, $(2,0)$, $( - 2,-2)$.

1. Step2: Plot on Cartesian - plane

On the Cartesian - plane, for the point $(1,1)$, move 1 unit to the right on the x - axis and 1 unit up on the y - axis. For $(-1,2)$, move 1 unit to the left on the x - axis and 2 units up on the y - axis. For $(0, - 3)$, stay at the origin on the x - axis and move 3 units down on the y - axis. For $(2,0)$, move 2 units to the right on the x - axis and stay at the origin on the y - axis. For $(-2,-2)$, move 2 units to the left on the x - axis and 2 units down on the y - axis.

Question 2:

1. Step1: Choose equations of lines

Let the equations of the lines be $y = x$, $y=-x + 1$, $y = 2x-2$.

1. Step2: Find points on lines

For $y = x$, when $x = 0,y = 0$; when $x = 1,y = 1$. For $y=-x + 1$, when $x = 0,y = 1$; when $x = 1,y = 0$. For $y = 2x-2$, when $x = 0,y=-2$; when $x = 1,y = 0$.

1. Step3: Graph the lines

Plot the points for each line and draw a straight line passing through them.

Question 3:

1. Step1: Let the two points be $(x_1,y_1)=(1,2)$ and $(x_2,y_2)=(3,4)$
2. Step2: Calculate the mid - point

The mid - point formula is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Substituting the values, we get $M=(\frac{1 + 3}{2},\frac{2+4}{2})=(2,3)$.

1. Step3: Calculate the distance

The distance formula is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substituting the values, $d=\sqrt{(3 - 1)^2+(4 - 2)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}$.

1. Step4: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the values, $m=\frac{4 - 2}{3 - 1}=\frac{2}{2}=1$.

Answer:

Question 1: Points $(1,1)$, $( - 1,2)$, $(0, - 3)$, $(2,0)$, $( - 2,-2)$ are plotted as described above.
Question 2: Lines $y = x$, $y=-x + 1$, $y = 2x-2$ are graphed as described above.
Question 3: Mid - point: $(2,3)$; Distance: $2\sqrt{2}$; Slope: $1$