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

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## Question:

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

Match each pair of points A and B to point C such that the measure of Angle ABC=90*.
Tiles
1. A(3, 3) and B(12, 6)
2. C(6, 52)
3. A(-10, 5) and B(12, 16)
4. C(16, -6)
5. A(-8, 3) and B(12, 8)
6. C(18, 4)
7. A(12, -14) and B(-16, 21)
8. C(-11, 25)
9. A(-12, -19) and B(20, 45)
10. A(30, 20) and B(-20, -15)

## Answer:

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

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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
————————————————————————————————————–

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
———————————————————————————————————–

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

From the answer and question examples above, hopefully, they might be able to guide the student deal with the question they had been looking for and keep in mind of every single thing stated in the answer above. You could certainly then have a discussion with your classmate and continue the school learning by studying the question jointly.