Draw a Right Triangle
Part 1
Using graph paper draw a right triangle given the following coordinates.
A(1,7) B(1,-1) C(7,-1)
(i got the triangle from this)
Part 2
Now, on the same graph paper using the same axes, translate (slide) the triangle 5 spaces along the x-axis (to the right) and 9 spaces along the y-axis (down) and name this new triangle XYZ.
State the new coordinates of the triangle.
X(6,-2)
Y(6, -10)
Z(12, -10)
(I got the triangle from this)
(what do I do for the next two parts of this assignment?)
Identify the 6 congruent parts between triangle ABC and triangle XYZ.
Using the distance formula verify that the corresponding sides are congruent.
o (i.e. verify that AB = XY, AC = XZ, and BC = YZ).
the three angles and the three sides are congruent.
Now for example check length of AB against XY
AB = sqrt[(1-1)^2 + (-1-7)^2 ]
= sqrt (-8^2) = 8
XY = sqrt[(6-6)^2 + (-10+2)^2 ]
= sqrt (-8^2) = 8 sure enough
To identify the congruent parts between triangle ABC and triangle XYZ, you can compare the lengths of their corresponding sides. Here's how you can do it:
1. Identify the corresponding sides:
- Triangle ABC: AB, AC, BC
- Triangle XYZ: XY, XZ, YZ
2. Using the distance formula, calculate the lengths of the corresponding sides. The distance formula is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's start by verifying AB = XY:
- For AB:
AB = √((x2 - x1)^2 + (y2 - y1)^2)
= √((1 - 1)^2 + (-1 - 7)^2)
= √(0^2 + (-8)^2)
= √64
= 8
- For XY:
XY = √((x2 - x1)^2 + (y2 - y1)^2)
= √((6 - 1)^2 + (-2 - (-1))^2)
= √((5)^2 + (-1)^2)
= √(25 + 1)
= √26
Since AB = 8 and XY = √26, they are not congruent.
Now, let's verify AC = XZ:
- For AC:
AC = √((x2 - x1)^2 + (y2 - y1)^2)
= √((7 - 1)^2 + (-1 - 7)^2)
= √((6)^2 + (-8)^2)
= √(36 + 64)
= √100
= 10
- For XZ:
XZ = √((x2 - x1)^2 + (y2 - y1)^2)
= √((12 - 6)^2 + (-10 - (-1))^2)
= √((6)^2 + (-9)^2)
= √(36 + 81)
= √117
Since AC = 10 and XZ = √117, they are not congruent.
Lastly, let's verify BC = YZ:
- For BC:
BC = √((x2 - x1)^2 + (y2 - y1)^2)
= √((7 - 1)^2 + (-1 - (-1))^2)
= √((6)^2 + (0)^2)
= √(36)
= 6
- For YZ:
YZ = √((x2 - x1)^2 + (y2 - y1)^2)
= √((12 - 6)^2 + (-10 - (-10))^2)
= √((6)^2 + (0)^2)
= √(36)
= 6
Since BC = 6 and YZ = 6, they are congruent.
In summary, out of the three corresponding sides, only BC = YZ is congruent. AB = XY and AC = XZ are not congruent.