Question

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.

Answer 1

When two lines intersect at 90° degrees angle, the lines are perpendicular to each other. Two perpendicular lines, their slope will give a product of -1

i.e. if the first's line slope is 5, then the second line's will be -1 ÷ 5 = -¹/₅

To find the slope of a line, we divide the vertical distance by the horizontal distance. 

We'll use the trial and error method to find the right pairing

Let's start with A(3, 3) and B(12, 6)

Vertical distance = 

Horizontal distance = 

The slope AB = ³/₉ = ¹/₃

We want BC to have a slope -1 ÷ ¹/₃ = -3

Try C(16, -6); check the slope with B(12, 6)

Vertical distance = 

Horizontal distance = 

Slope of BC = -12 ÷ 4 = -3

The slope BC = -3 is the value we want so, tile 1 pair with tile 4

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Let's do A(-10, 5) and B(12, 16)

Vertical distance = 16 - 5 = 11

Horizontal distance = 12 - -10 = 22

Slope AB = ¹¹/₂₂ = ¹/₂

The perpendicular slope would be -1 ÷ ¹/₂ = -2

Try C(18, 4)  with B(12, 16)

Vertical distance = 16 - 4 = 12

Horizontal distance = 12 - 18 = -6

Slope BC = ¹²/₋₆ = -2

Slope BC and slope AB perpendicular, so tile 3 matches with tile 6

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Let's try A(12, -14) and B(-16, 21)

Vertical distance = 21 - -14 = 35

Horizontal distance = -16 - 12 = -28

The slope AB = ³⁵/-₂₈ = ⁵/₋₄

We need the perpendicular slope to be -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

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Take A(-12, -19) and B(20, 45)

Vertical distance = 45 - -19 = 64

Horizontal distance = 20 - -12 = 32

Slope AB = ⁶⁴/₃₂ = 2

We need the perpendicular slope to be -1 ÷ 2 = -¹/₂

We have C(6, 52) and checking the slope with B(20, 45)

Vertical distance = 45 - 52 = -7

Horizontal distance = 20 - 6 = 14

The slope is ⁻⁷/₁₄ = -¹/₂

Tile 9 pairs with tile 2

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Conclusion

Tile 1 ⇒ Tile 4

Tile 3 ⇒ Tile 6

Tile 7 ⇒ Tile 8

Tile 9 ⇒ Tile 2

Tile 5 and Tile 10 do not have pairs