Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Functions - Linear models - gradient, distance and midpoint.
Test Yourself 1 - Solutions.


 

 

Given diagrams.

1.

(iii)

(iv)

(v)

 

2.

 

(iii)

(iv)

 

(v)

 
Drawing your own diagram. 3.

(iii) .

(iv) .

(v) .
 

4. The points are M (-5, -8) and N (10, 16).

(i)

(ii)

(iii)

  5. The points are A (-2, 1) and B (3, 1).

(i) There is no rise as the y values are the same.
Hence the gradient = 0.

(iv) Distance = 2 + 3 = 5.

(v) .
  6. The points are A (-1, 3) and B (-1, -2).

(i) The x values are the same and so the line rises vertically. There is no run. Hence the gradient cannot be defined.

(ii) Distance = 3 + 2 = 5.

(iii) .
Miscellaneous.

7. First draw the points approximately and indicate the vertical and horizontal distances just as for the previous questions.
 

8. First draw the points approximately and indicate the vertical and horizontal distances just as for the previous questions.
 

9.

A check shows both sets give the required distance.
They are points on the circle with centre at L corresponding to an x value of -6.
One line has a gradient of 1.1 (when the point is (-6, -2) and so below L).
The line has a gradient of -0.5 (when the point is (-6, 8) and so above L).

 

10. Midpoints are calculated by finding the average of the x values and then the average of the y values.