Question

Two points A (-2, 9) and B (4, 8) lie on a line l. (i) Find the slope of the line l. (ii) Find the coordinates of the midpoint of the points A and B (iii) Find the distance between points A and B.

Answer 1

Answer:

$m=-\frac{1}{6} \approx -0.1667$

$M=(1,\frac{17}{2} )=(1,8.5)$

$d=\sqrt{37} \approx 6.083$

Step-by-step explanation:

(i) For two different points on a line, the slope m is defined as the difference on the y-axis divided by the difference on the x-axis:

$m=\frac{\Delta y}{\Delta x} =\frac{y_2-y_1}{x_2-x_1}$

Where:

$(x_1,y_1)=(-2,9)\\\\(x_2 , y_2)=(4,8)$

So:

$m=\frac{8-9}{4-(-2)} =\frac{-1}{6} \approx -0.1667$

(ii)

To find the coordinates of the midpoint, you can use the following formula:

$M=(\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )$

Therefore:

$M=(\frac{-2+4}{2} , \frac{9+8}{2} )=(\frac{2}{2} , \frac{17}{2} ) =(1,8.5 )$

(iii) The distance between two points is given by the following formula:

$d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }$

Hence:

$d=\sqrt{(4-(-2))^{2}+(8-9)^{2} } =\sqrt{(6)^{2}+(-1)^{2} } =\sqrt{36+1} =\sqrt{37} \\\\d\approx 6.083$