Answer:
8. 20.8 units
9. isosceles
Step-by-step explanation:
8.
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.)
slant sides
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
horizontal side
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).
perimeter
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.
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9.
Sides PR and QR are congruent, so the triangle is isosceles.
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Additional comment
A triangle whose vertices are integer grid coordinates cannot be equilateral.
