The point (-7, 4) is reflected over the line x= -3. Then, the result point is reflected over the line y = x. Where is the point located after both reflections? A. (-10, 7)
B. (1, 4)
C. (4, -7)
D. (4, 1)

D. (4, 1)

Step-by-step explanation:

When we have a reflection over a line, the perpendicular distance to that line is invariant.

Then, if we have the point

(-7, 4) and we have a reflection over the line x = -3

The distance between the x component and the line is:

I -7 - (-3)I = 4

Then the reflected point will also be at a distance of 4 units to the line x = 3, and this is at the point x = 1.

Then the new point is (1, 4)

Now we do a reflection over the line x = y.

This type of reflection just changes the x-component by the y-component, and the y-component by the x-component.

Then the new point will be (4, 1)

Then the correct option is D.

6.68km/litre

Step-by-step explanation:

Distance(d) = 187km ( to 3 significant figures)

Petrol(p) = 28litres ( to 2 significant figures)

A number, x, rounded to 1 significant figure is 200

Write down the error interval for x

Calculating the lower and upper bound for both 'd' and 'p'

Upper bound 'd' = 187.5km

Lower bound 'd' = 186.5km

Upper bound 'p' = 28.5km

Lower bound 'p' = 27.5km

Therefore,

Petrol consumption (C) = d/p

Upper C = 187.5 / 28.5 = 6.57894

Lower C = 186.5 / 27.5 = 6.781818

Accuracy answer for C = (6.57894 + 6.781818) / 2 = 6.680379

= 6.68km/ litre ( to 3 significant figures)

To achieve a reasonable level of accuracy, the upper and lower bounds of P and D was used to calculate C, which was then averaged.

Using 3 significant figures ensure that we capture the C better, instead of early rounding.