What is the value of x in the equation 8x-5(x-1)=20 1. 25/3 2. 21/4 3. 5 4. 7
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The first (and most typical) way to find distance of two points is by using the distance formula.
One alternative is the Manhattan metric, also called the taxicab metric. This option is much more complicated, and rarely used in high school math. d(x,y)=∑i|xi-yi|
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:
Finally we have to translate it 1 unit up towards positive y values so we have to add 1 to its y coordinate:
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:
