Hi :) how to do question 7 ?

Step-by-step explanation:

We khow that the equation of a circle is written this way :

(x-a)²+(y-b)²=r² where (x,y) are the coordinates of the cercle's points and (a,b) the coordinates of the cercle's center and r the radius .

Our task is to khow the values of a and b :

We khow that the center is lying on the line 3x+2y=16⇒ 2y=-3x+16⇒ y= x+8  We khow that the points P and Q are two points in the cercle Let Ω be the center of this cercle we can notice that : PΩ AND QΩ are both equal to the radius ⇒ PΩ=QΩ= rSo let's write the expression of this distance using vectors KHOWING THAT Ω(a,b)Vector PΩ(a-4,b-6) and Vector QΩ(a-8,b-2) PΩ=and QΩ=Let's substitute a by x and b by y PΩ=QΩ we substitute each distance by its expression After simplyfying the expressions we get finally : -12+8x-8y=0 now we have -12x +8x-8y=0 and the line equation 3x+2y-16=0 these are simultanious equations so after solving them we get x=3.8 wich is approximatively 4 and y=2 we substitute a by 4 and y by 2 in PΩ to get the radius we get r = = 4 so r²= 16 then the equation is : (x-4)²+(y-2)²=16

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.