# Get questions and answers for Precalculus

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Sketch the region in the xy-plane.

h(x, y)||x| < 3 and |y| < 2}

Sketch the region in the xy-plane.

{(x, y) | 0 < y < 4 and x < 2}

Sketch the region in the xy-plane.

{(x, y) | y > 2x - 1}

Sketch the region in the xy-plane.

{(x, y) |1 + x < y < 1 - 2x}

Sketch the region in the xy-plane.

{(x, y)|2x < y < 1/2 (x + 3)}

Find a point on the y-axis that is equidistant from (5, -5) and (1, 1).

Show that the midpoint of the line segment from P1(x1, y1) to P2(x2, y2) is (x1 + x2/2, y1 + y2/2)

Find the midpoint of the line segment joining the given points.
(a) (1, 3) and (7, 15)

(b) (-1, 6) and (8, -12)

Find the lengths of the medians of the triangle with vertices A(1, 0), B(3, 6), and C(8, 2). (A median is a line segment from a vertex to the midpoint of the opposite side.)

Show that the lines 2x - y = 4 and 6x - 2y = 10 are not parallel and find their point of intersection.

Show that the lines 3x - 5y + 19 = 0 and 10x + 6y - 50 = 0 are perpendicular and find their point of intersection.

Find an equation of the perpendicular bisector of the line segment joining the points A(1, 4) and B(7, -2).

(a) Find equations for the sides of the triangle with vertices P(1, 0), Q(3, 4), and R(-1, 6).
(b) Find equations for the medians of this triangle. Where do they intersect?

(a) Show that if the x- and y-intercepts of a line are nonzero numbers a and b, then the equation of the line can be put in the form x/a + y/b = 1
This equation is called the two-intercept form of an equation of a line.
(b) Use part (a) to find an equation of the line whose x-intercept is 6 and whose y-intercept is -8.

A car leaves Detroit at 2:00 pm, traveling at a constant speed west along I-96. It passes Ann Arbor, 40 mi from Detroit, at 2:50 pm.
(a) Express the distance traveled in terms of the time elapsed.
(b) Draw the graph of the equation in part (a).
(c) What is the slope of this line? What does it represent?

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