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*. Tiles1. 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)
Accepted Solution
A:
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 = [tex]y_B-y_A=6 - 3 = 3[/tex] Horizontal distance = [tex]x_B-x_A=12-3=9[/tex] 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 = [tex]y_C-y_B=-6-6=-12[/tex] Horizontal distance = [tex]x_C-x_B=16 - 12 = 4[/tex] Slope of BC = -12 ÷ 4 = -3
The slope BC = -3 is the value we want so, 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
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