geometry Q: Find lengths of Highways 1 and 4, given....

[confusedintexas]

My daughter needs help and neither me or her father can help. No answer just maybe a formula or intructions?

The city of Springfield is 5 miles west and 3 miles south of Capital City, while Brighton is 1 mile east and 4 miles north of Capital city. Highway 1 runs straight between Brighton and Springfield; Highway 4 connects Springfield and Capital City. Find the length of Highway 1. How long is Highway 4?

 

[stapel]

A good start might be to draw the picture, and then see what right-angle relationships you can find. :idea:

Eliz.

 

[skeeter]

as stated previously ... a sketch helps.

both problems involve use of the Pythagorean theorem.

for highway 1, note that Brighton is 6 miles east and 7 miles north from Springfield.

for highway 4, note that Cap City is 5 miles east and 3 miles north from Springfield.

 

[Mrspi]

You might want to draw a diagram on a coordinate plane, with Springfield located at the origin (0, 0).

East is generally considered to be to the right, west to the left, north going up, and south going down.


So, if Brighton is 6 miles east and 7 miles north of Springfield, that would make the coordinates of Brighton (6, 7).

Do the same thing to locate the coordinates of Cap City.

Then, you can use the formula for the distance between the two points which represent the locations of Brighton and Cap City:

If two points have coordinates (x<SUB>1</SUB>, y<SUB>1</SUB>) and (x<SUB>2</SUB>, y<SUB>2</SUB>), the distance D between them is

D = sqrt[ (x<SUB>2</SUB> - x<SUB>1</SUB>)<SUP>2</SUP> + (y<SUB>2</SUB> - y<SUB>1</SUB>)<SUP>2</SUP> ]

In the future, it would probably be best if you had your daughter post here directly....working through a "third party" is seldom successful. We need to see what your daughter is thinking and how she is approaching these problems in order to try to help her effectively.