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 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 = $y_B-y_A=6 - 3 = 3$
Horizontal distance = $x_B-x_A=12-3=9$
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 = $y_C-y_B=-6-6=-12$
Horizontal distance = $x_C-x_B=16 - 12 = 4$
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

Answer 2

To match each pairs A and B to point C to make the measures of angles ABC= 90 degrees will be:

• Tile 1 matches Tile 4.
• Tile 3 matches Tile 6.
• Tile 7 matches  Tile 8.
• Tile 9 matches Tile 2.
• Tile 5 and 10 do not have pairs.

What are pairs?

A pair is a composition of the x- coordinates and the y-coordinates having two values written in a fixed order within a parenthesis.

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.

Using the trial and error method to find the right pairing:

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

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)

Slope of BC = -12 ÷ 4 = -3

• Tile 1 pair with Tile 4

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

• 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

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

Learn more about pairs here:

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