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Part 2 Directions: Tell whether the lines are parallel, perpendicular, or neither. Show all work. 5.) Line 1: through (7,3) and (8,7) Line 2: through (-5,-4) and (-1,-5) 6.) Line 1: through (5,2) and (1, -7) Line 2: through (-1, 3) and (9,-1) 7.) Line 1: through (5,9) and (7, 13) Line 2: through (0, 2) and (4, 10)

User Chris Rogers
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1 Answer

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The first two points are

(7,3) and (8,7) --- line 1

(-5, -4) and (-1,-5)---- line 2

we can only determine whether a line is parallel, or perpendicular through slope

slope = y2 - y1/ x2 - x1

x1 = 7, y1 = 3 , x2 = 8, and y2 = 7

slope = 7 - 3 / 8 - 7

slope = 4 / 1

slope = 4

for the first line the slope is 4

second line

x1 = -5, y1 = -4, x2= -1, and y2 = -5

slope = -5 -(4) / -1 - (-5)

slope = -5 + 4/ -1 + 5

slope = -1 /4

slope = -1/4

slope is perpendicular when

m1 x m2 = -1

slope is parallel when

m1 = m2

for the first question the slope is perpendicular because

4 x -1/4 = -1

therefore line 1: (7,3) and (8,7) and line 2: (-5,-4) and (-1,-5) are perpendicular

question 2

(5,2) and (1,7) for the first line

(-1,3) and (9,-1) for the second line

slope = y2 - y1 / x2 - x1

slope = 7 - 2 / 1 - 5

slope = 5 / -4

for line 1 slope is -5/4

slope for line two

slope = y2 - y1/ x2 - x1

slope = -1 - 3/ 9 -(-1)

slope = -4 / 9 +1

slope = -4/10

slope = -2/5

since slope 1 and slope 2 are not the same, therefore the lines are not parallel

for perpendicular

-5/4 x -2/5 = 1/2

they are not perpendicual because the product of the two slopes is not equals to -1

last question

line one : (5,9) and (7,13)

line two: (0,2) and (4,10)

for line 1

slope = y2 - y1/ x2 - x1

slope = 13 - 9/ 7 - 5

slope = 4 / 2

slope = 2

for line 1 slope is 2

for line 2

slope = 10 - 2 / 4 - 0

slope= 8 /4

slope = 2

for line two slope is 2

therefore slope 1 and slope 2 are equal

slope 1 = slope 2

the lines are parallel to each other

User Marek Dorda
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2.9k points