The triangles below are congruent and their corresponding parts are marked.
1 answer:
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Answer:
a. 1,000 yards
b. (2, -1)
Step-by-step explanation:
Coordinates of Ben's House = (6, 2)
Coordinates of Kate's House = (-2, -4)
a. Number of yards between Kate and Ben's House using instance formula, .
1 unit = 100 yards
Therefore, 10 units = 1,000 yards.
Kate and Ben's House are 1,000 yards apart.
b. Since Jason's home is halfway between Ben and Kate's House, therefore, Jason's location is the midpoint between Ben and Kate's House. Use the midpoint formula to calculate the coordinates of Jason's location on the map, using (6, 2) and (-2, -4).
Plug in the values
9514 1404 393
Answer:
1. line b is perpendicular to the other two, which are parallel
2. line a is perpendicular to the other two, which are parallel
Step-by-step explanation:
1. The differences between coordinates (∆x, ∆y) are ...
(-2, 3) -(1, -1) = (-3, 4) . . . line a
(-3, 1) -(1, 4) = (-4, -3) . . . line b
(0, 2) -(3, -2) = (-3, 4) . . . line c
When the (∆x, ∆y) values are identical, the lines are parallel. If the values are swapped, and one differs in sign, the lines are perpendicular.
line b is perpendicular to lines a and b, which are parallel
__
2. When all of the equations are written in standard form, they are ...
- 4x +y = 7 . . . line a
- x -4y = 2 . . . line b
- x -4y = 3 . . . line c
As above, when the x- and y-coefficients are identical, the lines are parallel. If they are swapped and one is negated, the lines are perpendicular.
line a is perpendicular to lines b and c, which are parallel
__
In the attached graph, the lines of part 1 are blue; those of part 2 are red.
