Answer:
8. 20.8 units
9. isosceles
Step-by-step explanation:
<h3>8.</h3>
The vertical altitude line divides the triangle into two congruent right triangles. Each has a horizontal leg of 4 units, and a vertical leg of 5 units. (You can find these lengths by subtracting coordinates, or by counting grid squares.)
<u>slant sides</u>
The hpotenuses of these right triangles are the short sides (PR, QR) of the larger triangle PQR. We can find their length using the Pythagorean theorem. Defining S as point (-2, -1), we have ...
PS² +SR² = PR² . . . . . . . . . . . . the Pythagorean theorem relation
4² +5² = PR² = 16 +25 = 41 . . . with numbers filled in
PR = √41 . . . . . . . . . . . . . . take the square root
PR ≈ 6.4 . . . . . . . . . . . round to tenths
<u>horizontal side</u>
The length of side PQ is 8 units, found by subtracting x coordinates ((2 -(-6)) = 8), by counting grid squares, or by doubling the length of PS (2(4) = 8).
<u>perimeter</u>
The perimeter of the triangle is the sum of its side lengths:
perimter = PR +QR +PQ = 6.4 +6.4 +8 = 20.8
The perimter of triangle PQR is 20.8 units.
__
<h3>9.</h3>
Sides PR and QR are congruent, so the triangle is isosceles.
_____
<em>Additional comment</em>
A triangle whose vertices are integer grid coordinates cannot be equilateral.
