Geometry help?

Question

1. Renae travels 4 miles due east from her house, then travels 6 miles due south. Measured directly, how many miles is she from her house? Leave your answer in RADICAL FORM.

2. The distance between point A and B is 5 sqrt 5 units. If point A (-4, -7) and point B (x, 3), what is the value of the x-coordinate of Point B? Point B is in Quadrant 1.

can anybody show me how to do these 2 problems step by steps? thanks.

Answer 1

1) It's a right-angle triangle - one side is 4 the other is 6, what is the hypotenuse? This is easy. Draw a triangle - one side 4, right angle, next side 6. The hypotenuse is the "square root of the sum of the squares".
SQRT(4*4 + 6*6) or SQRT(16+36) = SQRT(52)
52 is 4*13 so the answer is 2*SQRT(13)

2) Again, you have a right-angle triangle. (Duh. This is what you are studying, nyet?)
One end of the hypotenuse is at -4,-7. The other is at x, 3.
We are given a length of 5*SQRT(5). Call this side C.
So, assuming we go UP first,
the one side A is from -4, -7 to x,-7. (should be in Quad 2) this is a length of (x+4)
Do a 90 degree turn right to Quad 1
the other side B is from x,-7 to x,3. This is a length of 10.

...from A^2 + B^2 = C^2 - our buddy Pythagoras again.
(x+4)^2 + 10^2 = (5*SQRT(5))^2
(x+4)^2 + 100 = 125 - don't bother expanding the (x+4)^2
(x+4)^2 = 25 - simplified.
x+4 = 5 - took sqrt of each side.
x=1 - pretty simple. No quadratic solution required.

Answer 2

1. 4^2+6^2=c^2 (pythagorean theorem) ^ means to the power of....
c=4 x the suare root of ten miles

2.what does sqrt mean?