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Pretend you are asked to draw a rectangle on the coordinate plane shown above. Three of its vertices are (1, -5), (1, -2), and (6, -5). Which of the following is the coordinate of the fourth vertex?

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chetankachana

Answer:

(6,-2)

Step-by-step explanation:

I'll have the coordinate plane shown in an attachment.

But what I want you to know is, that you don't need to graph it.

We have to different x-values, 1 and 6. We know that. But since the sides are vertical, they are pairs. That's why there is a pair of coordinates that have an x-value of 1.

Similarly, we have pairs of y-values of -5, because they are horizontal sides.

Now, the only un-paired values is x-value of 6, and y-value of -2.

There's your coordinate: (6,-2)

-Chetan K

Ver imagen chetankachana

Let the rectangle be ABCD

  • A(1,-5)
  • B(1,-2)
  • C(6,-5)
  • D(x,y) be other one

As AB||CD

  • slope of AD=slope of BC

[tex]\\ \rm\rightarrowtail \dfrac{y+5}{x-1}=\dfrac{5+2}{6-1}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{y+5}{x-1}=\dfrac{7}{5}[/tex]

[tex]\\ \rm\rightarrowtail 5y+25=7x-7[/tex]

[tex]\\ \rm\rightarrowtail 5y=7x-32[/tex]

  • x remains 6

[tex]\\ \rm\rightarrowtail 5y=-10 [/tex]

[tex]\\ \rm\rightarrowtail y=-2[/tex]

  • (x,y)=(6,-2)
Ver imagen Аноним

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