What transformation with it or made it to ABC produce XYZ assess whether the two triangles are congruent how do you know? A(-5,2), B (-3,2), C(-3,5) Z(-3,-4), Y(0,-4); X (0,-6)

Answer 1

To determine whether the two triangles are congruent, we can assess if they have equal side lengths and equal angles.

First, let's calculate the side lengths for both triangles.

Triangle ABC:
- Side AB: Distance between A(-5,2) and B(-3,2) = 2 units
- Side BC: Distance between B(-3,2) and C(-3,5) = 3 units
- Side CA: Distance between C(-3,5) and A(-5,2) = √10 units (using the distance formula: √((x2-x1)^2 + (y2-y1)^2))

Triangle XYZ:
- Side YZ: Distance between Y(0,-4) and Z(-3,-4) = 3 units
- Side ZX: Distance between Z(-3,-4) and X(0,-6) = 2 units
- Side XY: Distance between X(0,-6) and Y(0,-4) = 2 units

After comparing the side lengths, we can see that the triangle ABC and XYZ have three pairs of sides with equal lengths: AB = YZ, BC = ZX, and AC = XY.

Next, let's evaluate the angles for both triangles.

Triangle ABC:
- Angle A: Calculated using the slope of AB and AC
m_AB = (2-2)/(-3+5) = 0/2 = 0
m_AC = (2-5)/(-5+3) = -3/-2 = 3/2
tan(A) = |(m_AB - m_AC)/(1 + m_AB*m_AC)|
tan(A) = |(0 - 3/2)/(1+0)|
tan(A) = |-3/2|
A ≈ 56.31°

Triangle XYZ:
- Angle Y: Calculated using the slope of YZ and YX
m_YZ = (-4+4)/(0+3) = 0/3 = 0
m_YX = (-4+6)/(0-0) = 2/0 (undefined slope)
Therefore, Angle Y is a right angle (90°).

From angle comparison, we observe that angle A in triangle ABC and angle Y in triangle XYZ have different measures.

Based on the information above, we can conclude that the two triangles (ABC and XYZ) are not congruent because they have different measures of one of their angles.

Answer 2

For fun, x=-1.what are the coordinates for f after a reflection

Answer 3

To determine the coordinates of point F after a reflection, we need to know the line or axis of reflection. Without this information, we cannot provide the exact coordinates after reflection. Reflection can occur over any line, such as the x-axis, y-axis, or any arbitrary line.

If you can provide the line or axis of reflection, I will be able to accurately calculate the coordinates of point F after reflection.