A reflection over the line y=x implies exchanging the x and y coordinates of a point. For example if you take a generic point (a,b) then its reflection over y=x is (b,a). Our point is (-1,3) so its reflection over y=x is the point (3,-1).

Then we have to translate it two units left. Translating a point left means that we are moving towards negative x values so we need to substract 2 from the x coordinate:

$(3,-1)\rightarrow(3-2,-1)=(1,-1)$

Finally we have to translate it 1 unit up towards positive y values so we have to add 1 to its y coordinate:

$(1,-1)\rightarrow(1,-1+1)=(1,0)$

And these are the final coordinates. In the following picture you have the points you get after each step (from A to D) with the y=x line in blue:

4 0

8 months ago

On a trip, a motorist drove 150 miles in the morning and 50 miles in the afternoon. His average rate in the morning was twice hi

Lina20 [59]

Answer:

Morning's average rate = 50 mph, and Afternoon's average rate = 25 mph.

Step-by-step explanation:

Suppose he drove 150 miles for X hours, then his average rate in the morning was (150/X) mph.

Given that he spent 5 hours in driving.

And he drove 50 miles for (5-X) hours, then his average rate in the afternoon was 50/(5-X) mph.

Given that his average rate in the morning was twice his average rate in the afternoon.

(150/x) = 2 * 50/(5-x)

150/x = 100/(5-x)

Cross multiplying terms, we get:-

150*(5-x) = 100*x

750 - 150x = 100x

750 = 100x + 150x

750 = 250x

x = 750/250 = 3.

It means he spent 3 hours in the morning and 2 hours in the afternoon.

So morning's average rate = 150/3 = 50 mph.

and afternoon's average rate = 50/(5-3) = 25 mph.

8 0

2 years ago

<img src="https://tex.z-dn.net/?f=%20543_%7Bx%7D%20%3D%20%20244_%7Bx%7D%20%2B%20%20255_%7Bx%7D%20%5C%3A%20find%20%5C%3A%20the%20

Westkost [7]

Will u be my frndd........??

8 0

2 years ago