Which pairs of lines are perpendicular? b) 3y=x+3 and y+3x=1. d) y+4x=2 and y−4x=1. f) y=5x+3 and y=−5x+1…

Question

Which pairs of lines are perpendicular? b) 3y=x+3 and y+3x=1. d) y+4x=2 and y−4x=1. f) y=5x+3 and y=−5x+1. 2). Another line L2 passes through (−2, 1) perpendicular to L1, draw the two lines, mark the point of intersection. Is perpendicular to another line

ScanSolve AI Tutor · Accepted Answer

Ili kubaini kama jozi za mistari ni wima (perpendicular), tunahitaji kulinganisha miteremko yao. Mistari miwili ni wima ikiwa bidhaa ya miteremko yao ni $-1$ .

a) Mstari unaopita kwenye pointi $(3, 3)$ na $(5, -1)$ ; na mstari unaopita kwenye pointi $(2, 0)$ na $(4, 1)$

Pata mteremko wa mstari wa kwanza.
Mstari wa kwanza unapita kwenye pointi $(3, 3)$ na $(5, -1)$ .
$m_1 = \frac{-1 - 3}{5 - 3} = \frac{-4}{2} = -2$
Mteremko wa mstari wa kwanza ni $m_1 = -2$ .
Pata mteremko wa mstari wa pili.
Mstari wa pili unapita kwenye pointi $(2, 0)$ na $(4, 1)$ .
$m_2 = \frac{1 - 0}{4 - 2} = \frac{1}{2}$
Mteremko wa mstari wa pili ni $m_2 = \frac{1}{2}$ .
Zidisha miteremko.
$m_1 \cdot m_2 = (-2) \cdot \left(\frac{1}{2}\right) = -1$
Hitimisho.
Kwa kuwa bidhaa ya miteremko ni $-1$ , mistari hii ni wima.
$\boxed{\text{Mistari ni wima}}$

Kumbuka: Sehemu za c) na e) hazionekani kwenye picha uliyotuma.

Which pairs of lines are perpendicular? b) 3y=x+3 and y+3x=1. d) y+4x=2 and y−4x=1. f) y=5x+3 and y=-5x+1. 2). Another line L2 passes through (-2, 1) perpendicular to L1, draw the two lines, mark the point of intersection. Is perpendicular to another line

Step-by-step solution

Pata mteremko wa mstari wa kwanza.

Pata mteremko wa mstari wa pili.

Zidisha miteremko.

Hitimisho.

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