Question

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?

Answer 1

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

`\\ \rm\rightarrowtail (y+5)/(x-1)=(5+2)/(6-1)`

`\\ \rm\rightarrowtail (y+5)/(x-1)=(7)/(5)`

`\\ \rm\rightarrowtail 5y+25=7x-7`

`\\ \rm\rightarrowtail 5y=7x-32`

• x remains 6

`\\ \rm\rightarrowtail 5y=-10`

`\\ \rm\rightarrowtail y=-2`

• (x,y)=(6,-2)

Answer 2

(6,-2)

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