O-LevelAdditional MathematicsStraight line graphs4037/22 · Oct/Nov 2023 · Q17 Marks
A straight line passes through the points (4, 23) and (-8, 29). Find the point of intersection, P, of this line with the line y = 2x+5.
- (a)A straight line passes through the points (4, 23) and (-8, 29). Find the point of intersection, P, of this line with the line y = 2x+5.[5]
- (b)Find the distance of P from the origin.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [M1] for m = (29-23)/(-8-4) oe or -1/2
- [M1] FT for (y-23)/(x-4) = their(-1/2) oe or y = their(-1/2)x + c and 23 = -1/2 x 4 + c oe
- [A1] y = -1/2 x + 25 isw
- [M1] Solves their linear equation simultaneously with y = 2x + 5 to find x or y
- [A1] (8, 21)
- [M1] FT their (8, 21) for √8² + 21² oe
- [A1] √505 isw or 22.5 or 22.47[22...] rot to 2 or more dp
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