Mathematics: Is the line through points p(–8, –10) and q(–5, –12) perpendicular to the line through points r(9, –6) and s(17, –5)? explain.

Is the line through points p(–8, –10) and q(–5, –12)

ninaa8748

06.01.2022

No, the line through points P(–8, –10) and Q(–5, –12) is not perpendicular to the line through points R(9, –6) and S(17, –5).

Step-by-step explanation:

Two lines are called perpendicular to each other if the product of their slope is -1.

Since, the slope of a line having end points (x_1,y_1) and (x_2,y_2) is,

$m=\frac{y_2-y_1}{x_2-x_1}$

Thus, the slope of line Joining points P(–8, –10) and Q(–5, –12),

$m_1=\frac{-12+10}{-5+8}=\frac{-2}{3}=-\frac{2}{3}$

While, The slope of line Joining points R(9, –6) and S(17, –5),

$m_2=\frac{-5+6}{17-9}=\frac{1}{8}$

Since,

$m_1\times m_2=-\frac{2}{3}\times \frac{1}{8}=-\frac{1}{12}\neq -1$

Thus, the line through points P(–8, –10) and Q(–5, –12) is not perpendicular to the line through points R(9, –6) and S(17, –5).

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nelly1078

06.02.2021

the volume is 504

Step-by-step explanation:

volume=1/2a*b*h

a=8

b=9

h=14

1/28*9*14=504

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