Use plotting and distance together on bigger problems: points in a line, squares and midpoints.
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Cards for the origin, the axes and other key ideas.
Questions from easy to hard across the chapter.
What are the coordinates of the point of intersection of the two coordinate axes?
Use distances to check whether three points lie on one straight line.
Check if the points M(-3, -4), A(0, 0), and G(6, 8) are on the same straight line without plotting. Guide: Compute the distances MA, AG, and MG, then check if .
List the coordinates of the three points provided.
State the distance formula and the condition for three points to be collinear.
Substitute the coordinates into the formula for MA, AG, and MG.
Show the arithmetic to find the final distance values for MA, AG, and MG.
State whether they form a line and provide your final logic.
Prove whether four points make a square, and find its area.
Plot the points A(2, 1), B(-1, 2), C(-2, -1), and D(1, -2). Is ABCD a square? Explain why and find the area.
State clearly whether it is a square and provide the final area.
Show how you mathematically proved the shape using side lengths and diagonals instead of just guessing by eye.
Why might engineers need to calculate these distances rather than just looking at a printed blueprint?
Discover the rule for the midpoint, and use it to find a missing point.
Analyze this data: S(-3, 0), M(0, 0), T(3, 0) | S(2, 3), M(3, 4), T(4, 5). When M is the midpoint of ST, what is the connection between their coordinates? Use that connection to find the coordinates of B given that M(-7, 1) is the midpoint of A(3, -4) and B(x, y).
State the final coordinates for point B.
Explain the rule you discovered for the midpoint and show the algebra steps to find B.
Where might finding a midpoint be useful in computer programming or design?