Coordinates and midpoints

Foundation and Higher

The idea

A coordinate $(x, y)$ goes across first, then up. The midpoint of two points is the mean of their coordinates: from $(2, 5)$ to $(8, -1)$ it is $(5, 2)$ .

Read the $x$ -coordinate along the horizontal axis.
Then the $y$ -coordinate on the vertical axis.
Midpoint: add each pair of coordinates and halve.

Watch out Check the scale on each axis: one square is not always one unit.

See it worked

Worked exampleCalculator allowed1 mark

Point P has coordinates ( $-6$ , 4). What is the x-coordinate of P?

Coordinates are written in the order (x, y).
The first coordinate is $-6.$

Answer $-6$

Your turn

Question 1Non-calculator3 marks

The diagonals of rectangle ABCD intersect at M(3, $-2$ ). Vertex A is ( $-1$ , 5). Work out the coordinates of the opposite vertex C.

Question 2Non-calculator4 marks

A rectangle has consecutive vertices A $(-3,4)$ , B $(7,4)$ and C $(7,-6)$ .

(a) Write the coordinates of the fourth vertex.

(b) Find its area.

Question 3Non-calculator4 marks

A triangle has vertices A( $-2$ , 1), B(7, 1) and C(3, 9). Work out its area.

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