Question

7(a). The sum of three numbers is 81. The second number is twice the first. Given that the third number is 6 more than the second, find the numbers.
7(b). Given the points P(3,5) and Q(-5,7) on the cartesian plane such that R(x,y) is the midpoint of PQ, find the equation of the line that passes through R and perpendicular to PQ.

Accepted Answer

(a) Let the numbers be x,y,z. x+y+z=81. y=2x. z=y+6=2x+6. Substituting: x+2x+(2x+6)=81 → 5x+6=81 → 5x=75 → x=15. So the numbers are 15, 30 and 36.

(b) Midpoint R=((3-5)/2,(5+7)/2)=(-1,6). Gradient of PQ=(7-5)/(-5-3)=2/-8=-1/4. Since the required line is perpendicular to PQ, its gradient=4 (negative reciprocal). Equation: y-6=4(x-(-1)) → y-6=4x+4 → y=4x+10, or 4x-y+10=0.

WAEC Mathematics 2023 Theory — Question 7

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