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ValentinkaMS [17]
3 years ago
7

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 o

f the points A and B (iii) Find the distance between points A and B.
Mathematics
1 answer:
blagie [28]3 years ago
8 0

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

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