IGCSE›Cambridge IGCSE Maths›Mind mapsCoordinate GeometryCambridge IGCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsCoordinatesWritten as (x,y)(x, y)(x,y) in that orderxxx is the horizontal positionyyy is the vertical positionLengthPythagoras on the two coordinate differenceslength=(x2−x1)2+(y2−y1)2\text{length} = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}length=(x2−x1)2+(y2−y1)2Line segment is the hypotenuseMidpointAverage of the xxxs and of the yyys(x1+x22,y1+y22)\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)(2x1+x2,2y1+y2)(2,−3)(2,-3)(2,−3) and (8,5)(8,5)(8,5) give (5,1)(5, 1)(5,1)Coordinatespoints, lengths, midpoints(x,y)(x,y)(x,y)MMMWorked exampleDistance from (1,2)(1,2)(1,2) to (4,6)(4,6)(4,6)32+42=25\sqrt{3^2 + 4^2} = \sqrt{25}32+42=25Answer: 5Missing pointsRearrange the midpoint formula for the unknownCollinear: equal gradients between pairs of pointsSolved by calculation, not by reading a gridExam tipsShow the substitution for the method markMidpoint uses a sum, not a difference