IGCSE Math question test

Question

1. A train, 1750 metres long, is travelling at 55km/h. Calculate how long it will take for the whole train to completely cross a bridge that is 480 metres long. Give your answer in seconds, correct to the nearest second.
2. y is inversely proportional to the square of (x+3) . When x = 5, y = 0.375 . Find y in terms of x.
3. A is the point (6, 1) and B is the point (2, 7). Find the equation of the perpendicular bisector of AB. Give your answer in the form y=mx+c

Please help me solve these questions step by step. Video is ok. Thanks so much

Answer 1

To find the equation of the perpendicular bisector of a line segment given the coordinates of the endpoints of that segment you need to know a point (midpoint of the segment) and its slope (negative reciprocal of the slope of the segment).

A(6,1), B(2,7)

Midpoint of segment AB (average of x-coordinates, average of y-coordinates):

(4, 4)

Slope of segment: (7 - 1) / (2 - 6) = 6/-4 = -(3/2)

Slope of perpendicular: 2/3

Using point-slope:

y - 4 = (2/3)(x - 4)

y = (2/3)x - 8/3 + 12/3

y = (2/3)x+ 4/3

desmos.com/calculator/id5mcmmenj

For problem 1 concentrate on the tail of the train. How far has it traveled when if finally clears the bridge? You will have to convert km to meters and hours to minutes to seconds. Use d = rt, t = d/r.

What does it mean when two variables are inversely proportional? xy = k where k is a constant. As x goes up, y goes down and vice-versa.

(x + 3)²y = k (use values given for x and y to determine k, substitute for k and solve for y in terms of x.