Question

Help!!! how do i solve this

Answer 1

Answer:

  (a) 7.1

  (b) (5/2, 3/2)

  (c) 2

  (d) y = -x +4

Step-by-step explanation:

(a)

The length of AC is found using the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((5 -(-2))² +(-1 -0)²) = √(49 +1) = 5√2 ≈ 7.1

The length of AC is about 7.1.

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(b)

The midpoint has coordinates that are the average of the end point coordinates.

  midpoint BC = (B + C)/2 = ((0, 4) +(5, -1))/2 = (5, 3)/2

  midpoint BC = (5/2, 3/2)

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(c)

The slope is found using the slope formula.

  m = (y2 -y1)/(x2 -x1)

For points A(-2, 0) and B(0, 4), the slope of the segment between them is ...

  m = (4 -0)/(0 -(-2)) = 4/2 = 2

The slope of AB is 2.

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(d)

The slope of line BC is found in the same was as for AB.

  m = (-1 -4)/(5 -0) = -5/5 = -1

The y-intercept of the line is point B, at y=4. So, the equation of line BC is ...

  y = mx +b . . . . . where m is the slope, and b is the y-intercept

  y = -x +4