AABC has coordinates A (4, 3), B (4, 0) and C (7, 0). APQR has coordinates P (0, -1), Q (0, -2) and R (1, -2). Use the grid provided to draw each triangle, then determine the scale factor of APQR to ∆ABC.

Answer 1

To draw triangles ABC and PQR on the grid:

Triangle ABC with coordinates A (4, 3), B (4, 0), and C (7, 0):

- Plot point A at (4, 3)
- Plot point B at (4, 0)
- Plot point C at (7, 0)
- Connect the points to form triangle ABC

Triangle PQR with coordinates P (0, -1), Q (0, -2), and R (1, -2):

- Plot point P at (0, -1)
- Plot point Q at (0, -2)
- Plot point R at (1, -2)
- Connect the points to form triangle PQR

Now that both triangles are drawn on the grid, we can determine the scale factor by comparing the side lengths. The scale factor is the ratio of corresponding side lengths in the two triangles.

For triangle ABC, the lengths of AB, BC, and CA can be found using the distance formula:

AB = √((4-4)^2 + (3-0)^2) = √(0 + 9) = 3
BC = √((7-4)^2 + (0-0)^2) = √(9 + 0) = 3
CA = √((4-7)^2 + (3-0)^2) = √(9 + 9) = 3√2

For triangle PQR, the lengths of PQ, QR, and RP can be found using the distance formula:

PQ = √((0-0)^2 + (-1+2)^2) = √(0 + 1) = 1
QR = √((0-1)^2 + (-2+2)^2) = √(1 + 0) = 1
RP = √((0-1)^2 + (-1+2)^2) = √(1 + 1) = √2

Now we can compare the side lengths of the two triangles:

Scale factor = (PQ/AB) = 1/3 = 1/3

Therefore, the scale factor of triangle PQR to triangle ABC is 1/3.