True or False? On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4) .

True. On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4) .

True or False? The x -coordinate of the midpoint is equal to the mean of the x -coordinates of the two points.

True. The x -coordinate of the midpoint is equal to the mean of the x -coordinates of the two points. The y -coordinate of the midpoint is also equal to the mean of the y -coordinates of the two points.

What does the gradient of a line measure?

The gradient of a line measures the steepness of the line.

True or False? A line with a gradient of -4 is steeper than a line with a gradient of -5 .

False. A line with a gradient of -5 is steeper than a line with a gradient of -4 . The steeper line is the one with the bigger gradient value when you ignore negative signs.

True or False? A positive gradient means the line goes upwards from bottom left to top right .

True. A positive gradient means the line goes upwards from bottom left to top right .

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True or False?
On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4).

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True or False?
On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4).
True.
On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4).
Which coordinates would be $a$ units left and $b$ units down from the point $(x, y)$ ?
The coordinates $a$ units left and $b$ units down from the point $(x, y)$ would be $(x - a, y - b)$ .
State an expression for the coordinates of the midpoint between $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .
The midpoint between $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is given by the expression $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ .
True or False?
The x-coordinate of the midpoint is equal to the mean of the x-coordinates of the two points.
True.
The x-coordinate of the midpoint is equal to the mean of the x-coordinates of the two points.
The y-coordinate of the midpoint is also equal to the mean of the y-coordinates of the two points.
What does the gradient of a line measure?
The gradient of a line measures the steepness of the line.
True or False?
A line with a gradient of -4 is steeper than a line with a gradient of -5.
False.
A line with a gradient of -5 is steeper than a line with a gradient of -4. The steeper line is the one with the bigger gradient value when you ignore negative signs.
True or False?
The gradient of a line is equal to $\frac{change in y}{change in x}$ .
True.
The gradient of a line is equal to $\frac{change in y}{change in x}$ .
State the formula for the gradient of the line that passes through $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .
The formula for the gradient of the line that passes through $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .
The formula $m = \frac{y_{1} - y_{2}}{x_{1} - x_{2}}$ will also give the gradient.
True or False?
A positive gradient means the line goes upwards from bottom left to top right.
True.
A positive gradient means the line goes upwards from bottom left to top right.
True or False?
The gradient of the line which passes through $(4, 5)$ and $(1, 2)$ can be found by calculating $\frac{2 - 5}{4 - 1}$ .
False.
The gradient of the line which passes through $(4, 5)$ and $(1, 2)$ can not be found by calculating $\frac{2 - 5}{4 - 1}$ .
The order needs to be consistent. If the second coordinate is used first for the $y$ coordinates, then the second coordinate should be used first for the $x$ coordinates.
It should be either $\frac{2 - 5}{1 - 4}$ or $\frac{5 - 2}{4 - 1}$ .
State the formula for the length of the line segment between $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .
The formula for the length of the line segment between $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is $\sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$ .
This is just using Pythagoras' theorem on the line segment between the two points.
True or False?
The length of the line segment between $(4, - 1)$ and $(7, 6)$ can be found by calculating $\sqrt{{(4 - (- 1))}^{2} + {(7 - 6)}^{2}}$ .
False.
The length of the line segment between $(4, - 1)$ and $(7, 6)$ can not be found by calculating $\sqrt{{(4 - (- 1))}^{2} + {(7 - 6)}^{2}}$ . Each bracket should be the difference between the $x$ values or the $y$ values.
It should be $\sqrt{{(7 - 4)}^{2} + {(6 - (- 1))}^{2}}$ .

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