Free Printable Length Midpoint distance and gradient

1.

Which of the following is the correct midpoint formula given two endpoints (x₁, y₁) and (x₂, y₂)?

a)

b)

c)

d)

2.

What is the midpoint if the two endpoints are
A(3,5) and B(11,5)

a)

(14, 0)

b)

(7,1)

c)

(14, 1)

d)

(7, 5)

3.

What's the midpoint of the the line-segment starting at (4, 5) and ending at (-12, 5)?

a)

(-4, 5)

b)

(-8, 5)

c)

( 8, 2.5)

d)

(8, 5)

4.

What is the midpoint between (10, 9)
and (-10, -5)

a)

(10, 2)

b)

(0, -2)

c)

(0, 2)

d)

(2, -2)

5.

Find the y-coordinate of the midpoint of the line

a)

1

b)

2

c)

-2

d)

3

6.

What is the formula for finding the distance between two points given their coordinates?

a)

$\sqrt{\left(x_2+x_1\right)^2+\left(y_2+y_1\right)^2}$

b)

$\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

c)

$\sqrt{\left(x_2-x_1\right)^2-\left(y_2-y_1\right)^2}$

d)

$\sqrt{\left(x_2+x_1\right)^2-\left(y_2+y_1\right)^2}$

7.

Find the distance between

\left(1,-4\right)

and

\left(-2,3\right)

.

a)

$\sqrt{2}$

b)

$\sqrt{58}$

c)

$\sqrt{23}$

d)

$\sqrt{53}$

8.

What do you call the measure of the steepness of a line?

a)

Midpoint

b)

Radius

c)

Gradient

d)

Derivative

9.

Find the gradient between point $\left(3,7\right)$ and $\left(-2,5\right)$ .

a)

$\frac{2}{5}$

b)

$\frac{5}{2}$

c)

$-\frac{2}{5}$

d)

$-\frac{5}{2}$

10.

Find the coordinates of the midpoint of $\left(6,-3\right)$ and $\left(4,5\right)$ .

a)

$\left(2,-4\right)$

b)

$\left(-4,2\right)$

c)

$\left(1,5\right)$

d)

$\left(5,1\right)$

11.

What can you say about the gradient of a horizontal line?

a)

positive

b)

negative

c)

zero

d)

infinite

12.

What can you say about two lines having the same gradient?

a)

They are perpendicular.

b)

They are intersecting.

c)

They are parallel.

d)

They are nothing.

13.

If two lines are perpendicular then the product of their gradients is equal to....

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

$1$

d)

$-1$

14.

The equation of a line is $y=3x-4$ , find its gradient.

a)

$-4$

b)

$3$

c)

$-3$

d)

$4$

15.

What is the gradient of a line perpendicular to $y=\frac{1}{2}x+3$ ?

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

$2$

d)

$-2$

16.

Find the gradient of each line with the equation given:
$y=3x+2$

a)

1

b)

1.5

c)

2

d)

3

17.

Find the gradient of each line with the equation given:
$y=7-5x$

a)

5

b)

-5

c)

7

d)

-7

18.

Which of these lines has a negative gradient?

a)

The orange one

b)

The red one

c)

The blue one

d)

The green one

19.

What is the gradient of this line?

a)

2

b)

½

c)

-½

d)

-3

20.

Consider the equation:
y=-x+4
Identify the slope and
y-intercept.

a)

m=4, b=-x

b)

m=-x, b=4

c)

m=1, b=4

d)

m=-1, b=4

21.

Determine the slope between
(4,2) and (-3,5).

a)

3/1

b)

-7/3

c)

3/7

d)

-3/7

22.

Dev keeps a record in graph form of how far his car travels and the number of gallons
of gasoline it uses.
What is the slope of the graph?

a)

64

b)

128

c)

32

d)

16

23.

What is the definition of

Gradient of a Line?

a)

It is the measure of degrees of a line.

b)

It is the measure of length of a line.

c)

It is the measure of steepness of a line.

d)

It is the measure of strength of a line.

24.

When the line is upward sloping, the gradient is ___________ .

a)

Positive

b)

Negative

c)

Zero

d)

Undefined

25.

When the line is downward sloping, the gradient is ____________ .

a)

Positive

b)

Negative

c)

Zero

d)

Undefined

26.

When the line is a horizontal (flat), the gradient is _____________ .

a)

Positive

b)

Negative

c)

Zero

d)

Undefined

27.

What is the gradient of this line?

a)

2

b)

-2

c)

1/2

d)

-1/2

28.

What is the gradient of the line AD?

a)

4/5

b)

-4/5

c)

5/4

d)

-5/4

29.

What is the gradient of the line TU?

a)

5

b)

-5

c)

0

d)

undefined

30.

What is the gradient of the following slope

a)

-2

b)

-1/2

c)

2

d)

-1

31.

What is the gradient of this line

a)

4

b)

4/5

c)

-2

d)

-1/2

32.

Find the slope of the line.

a)

1/2

b)

-1/2

c)

2/1

d)

-2/1

33.

Calculate the gradient of the coordinates K(-21, -11) and L(4, 19).

a)

$-\frac{6}{5}$

b)

$\frac{6}{5}$

c)

$\frac{8}{3}$

d)

$-\frac{8}{3}$

34.

When the line is vertical, the gradient is _____________ .

a)

Positive

b)

Negative

c)

Zero

d)

Undefined

35.

The gradient of horizontal line is .........

a)

Always zero

b)

undefined

c)

Always positive

d)

Always negative

Length Midpoint distance and gradient

Total questions: 35

Worksheet time: 2hrs 34mins

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