53. DISCUSS - DISCOVER - WRITE: Distance from a Point to a Line Let L be the line 2x + 4y = 8, and let P be the point (3,4). (a) Show that the points Q(0, 2) and R(2, 1) lie on L. (b) Let u = QP and v = QR, as shown in the figure. Find w = proj, u. (c) Sketch a graph that explains why | u – w| is the dis- tance from P to L. Find this distance. (d) Write a short paragraph describing the steps you would take to find the distance from a given point to a given line. R

Q: Find an equation for the line in the form ax + by = c, where a, b, and c are integers with no factor…

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Q: Q2) Find the slope of the straight line L1 that passes through the points P1 (0, 6) and P2 (5, 2),…

A: In the given question we have to find the slope of two lines and also tell about that are they…

Q: r1(t) = (3, –6, 2) +t (-4, 2, –4) r2(t) = (-3, 3, – 10) + t (2, 1, 0) Find the point of…

A: Lines r1 and r2 can be rewritten as follows:

Q: 9) A line segment has endpoints at A(-4. 11) and B(2,3). Which of the following would be the…

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Q: aluate √y² ds where C is the line segment from (2,1,-4) to (4, 1, 5). C

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Q: . Plot each pair of points and compute the distance between them:(a) (1, 4) and (3, 2) (b) (2, 1)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: What is the equation of a circle with its center at (0,–2) and passing through the point (3, –5)?

A: Given,          The equation of a circle with its center at 0,-2 and passing through the…

Q: Find x and y if (2, 5) is the midpoint of points (x, y) and (-5, 6). b. Find the point (0, y) that…

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Q: Three or more points are collinear when they all lie on the same line. Use the steps below to…

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Q: Let A be the point with coordinates (-2, -1, -1) and let B be the point with coordinates (2, 0, 0).…

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Q: Find the y-intercepts: O (-1,0) and (3,0) O (5,0) and (0,-2) O (0,5) and (0, -2) O (0.-1) and (0,3)

A: Remember that y-intercept is the point on the graph where the curve cuts y-axis. i.e. ( 0 , f(0) )…

Q: (2,1) From the graph, find the midpoint of the line segment with endpoints of (- 2, 1) and (4, 3).…

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Q: 4. Determine the slope-intercept form the two points on the line. a) (3, – 1), (-6, - 4) b) (4,1),…

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Q: 13. The population of the nest of the aunt can triple in 8 weeks. If the population now is 12000,…

A: The formula for population of ants at time t (in weeks)Initial populationgrowth rate time in weeks

Q: Line L in the figure below is parallel to the line y=3x+2. Find the coordinates of the point P P=

A: First we find the slope of the given line:

Q: Find the distance the point P(0, 2, 8) is to the line through the two points Q(1,-1,4), and R(-1,-4,…

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Q: Q.I: (a) Find the equation of line that make angle 60° with y-axis and passes through (2, -1). (b)…

A: To solve a) equation of line.  b)to find intercepts.  c) Distance