Jinyu asked in Science & MathematicsMathematics · 2 months ago

# The slope of AB is =3/4 The slope of CD is 12/a Determine the value of a if AB丄CD?

Relevance
• 2 months ago

AB_|_CD=>(3/4)(12/a)=-1=>9/a=-1=>a=-9.

• alex
Lv 7
2 months ago

Rule

If (the slope of AB)*(the slope of CD)=-1

then

AB丄CD

• Philip
Lv 6
2 months ago

Suppose slope of AB = m. Then slope of CD which is perpendicular to AB is -(1/m), m =/= 0.

Here m = (3/4) so slope of CD = -(4/3) = 12/a. Then a = -(3/4)12 = -9.

• Anonymous
2 months ago

When solving questions as such, always keep in mind these two rules:

1) Parallel lines have the same slope.

2) Perpendicular lines have opposite reciprocals slopes:

m_1 x m_2 = -1

In this questions the lines are perpendicular so the second rule will be used:

AB丄CD

3/4 x 12/a = -1

dived 3/4 on both sides

12/a = -4/3

criss cross multiplication

-4a = 36

divide -4 on both sides

a = -9

• sepia
Lv 7
2 months ago

If two lines are perpendicular, the product of their gradients is -1.

i.e. (3/4) x (12/a) = -1

Hence, 9/a = -1

So, a = -9

• ?
Lv 7
2 months ago

Since AB ⊥ CD, the slope of CD must equal the negative reciprocal of the slope of AB.Since the slope of AB = 3/4, the slope of CD must equal

.....12......-4

.....---- = -----

......a........3

Therefore,

.....a = (12•3)/(-4)

.....a = -9..................ANS

• 2 months ago

Two lines are perpendicular if their slopes are negative reciprocals.

Therefore, the slope of CD is -4/3.

12/a = -4/3.

Cross-multiplying gives: -4a = 36.

a = -9