Think about placing your squares on a piece of graph paper, with all bottoms on the x axis. Let's place square A on the grid so it's lower left vertex is at (0,0). If square A has side length 4, it's top left corner is at (0,4) and the problem refers to this corner as point A. Square B is right next to square A, so it begins at x=4. It has a top left corner at (4,7) because its side length is 7. It is also 7 wide, so it ends at x = 4+7 = 11. This is where square C begins. It's left side is at x = 11. We only know it's side length is n, so its left corner is at (11,n) (and we will place it on the x axis, so our n is positive.)
So we have 3 points A (0,4); B (4,11); C (11,n)
If A, B and C are collinear, it means the points all lie on the same line.
There is a faster way I can do this problem, but all that matters is that YOU understand...So let's take it a step by step approach.
First, find the equation of line AB. An easy way is to just know the formula y = mx+b. Really, you can get to anywhere in this topic by knowing this one equation. A is on the line, so it's (x,y) pair must work in the y=mx+b of line AB. Same for B. So let's make 2 equations - one for point A and the other for point B, substituting what you know --
*from point A:: 4 = m(0) +b
*from point B:: 11 = m(4) + b
You have 2 equations with 2 unknowns. You can use substitution or elimination to solve for m and b.
Now, that you have m and b, you have the equation for line AB.
But C is on this very same line! So point C's (x,y) pair must also work in this same equation.
You can solve for the y coordinate of point C: Use y = mx + b, putting in the m and b you just found, and the substitute x=11 (from point C). The y you solve for is the n value of point C.
For the second part of the equation, just do it all again with the letters they are asking you to use. That is, start from the top, use a m for the number 4 (don't confuse this m for the slope in y=mx+b! This m is the length os square A. (Actually this is a poor choice for a letter in this instance. I suggest you use a capital M for the slope - as y=Mx+b, so you can see the difference between the m, variable, and the M, slope.) Use k for the number 7, and just keep these letters in the equations as you work through to solve for n.
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Bottom line: most students have already memorized y = mx +b. If not, learn it really well, and what the m and b are. The x and y just stand for the coordinates of any point on the line. Remember that if a point is on a line, that (x,y) pair MUST WORK in the equation. You can just keep using y = mx + b, rearrange as needed, or use to solve a system of equations, when you have a problem dealing with lines.
G_O_O_D L_U_C_K!!!!!!
Diane S.
08/18/19