The correct pairs in the boxes would be given as:
These are values that are known to have x and y coordinates written as values and matched in brackets.
We have perpendicularity, when two lines intersect at 90° degrees angle,
For the first
A(3, 3) and B(12, 6)
The slope AB = ³/₉ = ¹/₃
Then BC would have a slope -1 ÷ ¹/₃ = -3
For C(16, -6); and slope B(12, 6)
we have = -12 ÷ 4 = -3
Tile 1 and 4 are a pair.
For A(-10, 5) and B(12, 16)
we have Vertical distance = 16 - 5 = 11
we have Horizontal distance = 12 - -10 = 22
we have Slope = ¹¹/₂₂ = ¹/₂
then The perpendicular slope would be -1 ÷ ¹/₂ this gives us -2
For C(18, 4) and B(12, 16)
we would calculate the Vertical distance to be 16 - 4 = 12
also the Horizontal distance would be 12 - 18 = -6
then its Slope BC would be solved as = ¹²/₋₆ = -2
Tile 3 and 6 would be a match
Next we have A(12, -14) and B(-16, 21)
First we solve the Vertical distance = 21 - -14 = 35
Then we go for the Horizontal distance = -16 - 12 = -28
The slope = ³⁵/-₂₈ = ⁵/₋₄
We solve the perpendicular slope as -1 ÷ -⁵/₄ = ⁴/₅
Try C(-11, 25)
Vertical distance with B = 25 - 21 = 4
Horizontal distance with B = -11 - -16 = 5
The slope = ⁴/₅
Tile 7 matches tile 8
Take A(-12, -19) and B(20, 45)
First we solve the Vertical distance = 45 - -19 = 64
then we solve the Vertical distance = 20 - -12 = 32
Slope AB = ⁶⁴/₃₂ = 2
perpendicular slope to be -1 ÷ 2 = -¹/₂
We have C(6, 52) and checking the slope with B(20, 45)
First we solve the Vertical distance = 45 - 52 = -7
then we solve the Vertical distance Horizontal distance = 20 - 6 = 14
The slope is ⁻⁷/₁₄ = -¹/₂
This would give us a pair with tile 9 and 2.
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