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If A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4) form two line segments, AB and CD , which of these conditions needs to be met to prove that AB is perpendicular to CD?

see attachment for choices

If Ax1 y1 Bx2 y2 Cx3 y3 and Dx4 y4 form two line segments AB and CD which of these conditions needs to be met to prove that AB is perpendicular to CD see attach class=

Respuesta :

Nirina7
the answer is the third choice
it is c)
[y4-y3/x4-x3][y2-y1/x2-x1]= -1

proof
two lines are perpendicular if the product of their slope equals -1

Answer:

[tex]\frac{y_4-y_3}{x_4-x_3}\times \frac{y_2-y_1}{x_2-x_1}=-1[/tex]

Step-by-step explanation:

We know that,

If two line segments are perpendicular then the product of their slope is equal to -1,

Also, the slope of a line segment having the end points [tex](x_n,y_n)[/tex] and [tex](x_m,y_m)[/tex] is,

[tex]m=\frac{y_m-y_n}{x_m-x_n}[/tex]

So, the slope of line segment AB having end points [tex]A(x_1,y_1)[/tex] and [tex]B(x_2,y_2)[/tex] is,

[tex]m_1=\frac{y_2-y_1}{x_2-x_1}[/tex]

Similarly, the slope of line segment CD having end points [tex]C(x_3,y_3)[/tex] and [tex](x_4,y_4)[/tex] is,

[tex]m_2=\frac{y_4-y_3}{x_4-x_3}[/tex]

Hence, by the above property of perpendicular line segments ,

If AB and CD are perpendicular then,

[tex]m_1\times m_2=-1[/tex]

[tex]\implies \frac{y_4-y_3}{x_4-x_3}\times \frac{y_2-y_1}{x_2-x_1}=-1[/tex]

Third option is correct.

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