Question

What’s the length of QR?

Answer 1

8

Explanation:

Segment QR is on a vertical line, so the length of it can be found from the y-coordinates of Q and R. The length is simply the difference of the y-coordinates:

6 -(-2) = 8

QR is 8 units long.

You can also determine this by counting the grid squares along its length.

_____

Additional comment

Similarly, the length of a segment of a horizontal line is the difference of the x-coordinates of its end points. For example, PQ is 3 -(-4) = 7 units long. As with QR, you can also count grid squares to get this length.

When the segments are not vertical or horizontal, a formula based on the Pythagorean theorem can be used to find length. In some cases, these diagonal segments are the hypotenuse of a triangle you already have experience with. Segment ST, for example, is the hypotenuse of a 3-4-5 right triangle, so is 5 units long. Segment RS is the hypotenuse of an isosceles right triangle with side lengths 3, so is 3√2 units long.

Answer 2

8 units

Explanation:

If we start at point Q and count down to point R we find the distance of segment QR.

-> Since this is on a coordinate plane, we can also use the distance formula

d =
`\sqrt{(y_(2)- y_(1)) ^(2) +(x_(2)- x_(1))^(2) }`

d =
`\sqrt{(6--2) ^(2) +(3-3)^(2) }`

d =
`\sqrt{(6+2) ^(2) +(3-3)^(2) }`

d =
`\sqrt{(8) ^(2) +(0)^(2) }`

d =
`√(64)`

d = 8 units

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather