Can anybody help find the line of reflection??

I'll do part (a) to get you started. Part (b) will follow the same sort of steps.

In part (a), we have these two points

You can call the points any letters you want. Let's find the slope of line AB

m = (y2-y1)/(x2-x1)

m = (8-2)/(3-(-3))

m = (8-2)/(3+3)

m = 6/6

m = 1

The slope of line AB is 1.

The mirror line will have the negative reciprocal of this slope, so the slope of the mirror line is -1. In other words, the mirror line slope is perpendicular to line AB. We'll use this perpendicular slope later.

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Next, we find the midpoint of segment AB

Average the x coordinates to get (x1+x2)/2 = (-3+3)/2 = 0/2 = 0

Repeat for the y coordinates:  (y1+y2)/2 = (2+8)/2 = 10/2 = 5

The midpoint of AB is (0,5)

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The mirror line will have two defining traits

So,

y = mx+b

y = -1x+b ... plugging in that perpendicular slope

5 = -1*0+b .... plugging in (x,y) = (0,5)

5 = 0+b

b = 5

The equation of the mirror line is y = -x+5 as shown in the diagram below. The mirror line is shown in green. Point D isn't important as it's just used to help set up the 90 degree angle.

This wraps up part (a) and I'll let you handle part (b). If you're stuck, then feel free to ask.

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°

i wish i could you, i have no idea how to answer this

step-by-step explanation: