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neurologyYou need to know

• Coordinates are written as an ordered pair `(x, y)`, where `x` is the horizontal coordinate (abscissa) and `y` is the vertical coordinate (ordinate).
• The x-axis is horizontal and the y-axis is vertical; they intersect at the origin `(0, 0)`.
• In the first quadrant, both `x` and `y` are positive; in the second quadrant, `x` is negative and `y` is positive; in the third quadrant, both are negative; and in the fourth quadrant, `x` is positive and `y` is negative.
• Moving right increases `x`; moving left decreases `x`; moving up increases `y`; and moving down decreases `y` on a Cartesian grid.
• On the x-axis, the y-coordinate is 0, and on the y-axis, the x-coordinate is 0.
• Axes on coordinate grids must be labelled with variable names and marked with equal scale intervals; positive and negative directions must be indicated.
• The horizontal distance between two points with the same y-coordinate equals the absolute difference of their x-coordinates; the vertical distance between two points with the same x-coordinate equals the absolute difference of their y-coordinates.
• A horizontal straight line is parallel to the x-axis and has equation `y = b`; every point on the line has the same y-value, `b`.
• A vertical straight line is parallel to the y-axis and has equation `x = a`; every point on the line has the same x-value, `a`.
• The graph of `y = x` is a straight line through the origin with gradient 1; every point on it has equal coordinates `(x, x)`.
• The graph of `y = -x` is a straight line through the origin with gradient −1; every point on it has coordinates `(x, -x)`.
• The lines `y = x` and `y = -x` are perpendicular, and each makes a 45° angle with the coordinate axes.
• Reflecting a point in the y-axis changes `(x, y)` to `(-x, y)`; reflecting a point in the x-axis changes `(x, y)` to `(x, -y)`.
• The x-intercept of a graph is the point where `y = 0`; the y-intercept is the point where `x = 0`.
• Axis-aligned rectangles on a grid have opposite sides parallel to the axes; their vertices occur in pairs that share x-values and in pairs that share y-values.
• An axis-aligned square has four equal side lengths; adjacent vertices differ in only one coordinate by the common side length.
• In an axis-aligned right-angled triangle, the two legs lie on a horizontal and a vertical line, so two vertices share an x-value and two share a y-value.
• On `y = x`, increasing `x` by 1 increases `y` by 1; on `y = -x`, increasing `x` by 1 decreases `y` by 1.

• Draw and label perpendicular x- and y-axes with a ruler, marking the origin and equal scale intervals, and indicating positive and negative directions clearly.
• Plot points in the first quadrant by locating `x` along the x-axis, moving up by `y`, and marking the point accurately with a cross.
• Plot points in all four quadrants accurately by using the signs of `x` and `y` to choose the correct directions from the origin.
• Read and write the coordinates of a given point from a grid in the correct order `(x, y)`, including negative values.
• Identify the quadrant of a point and justify it using the sign pattern of its coordinates.
• Recognise, sketch, and label the lines `x = a` and `y = b` by drawing straight vertical or horizontal lines through the correct intercepts using a straightedge.
• Plot and label the graphs of `y = x` and `y = -x` across all four quadrants by generating at least two correct points for each and joining them with a straightedge through the origin.
• Determine the coordinates of missing vertices of an axis-aligned rectangle or square by using shared x- or y-values and equal side lengths.
• Use horizontal and vertical coordinate differences to calculate side lengths and verify whether a shape on the grid is a rectangle, square, or right-angled triangle.
• Find and label the intercepts of a line by substituting `x = 0` to get the y-intercept and `y = 0` to get the x-intercept.