Ple

two sidewalks in a park are represented by lines on a coordinate grid. two points on each of the lines are shown in the tables.
sidewalk 1
x y
2 8
0 3
sidewalk 2
x y
1 4
3 3
(a) write the equation for sidewalk 1 in slope-intercept form.
(b) write the equation for sidewalk 2 in point-slope form and then in slope-intercept form.
(c) is the system of equations consistent independent, coincident, or inconsistent? explain.
(d) if the two sidewalks intersect, what are the coordinates of the point of intersection? use the substitution method and show your work.

  (a)  y = 5/2x +3

  (b)  y = -1/2x +9/2

  (c)  consistent, independent

  (d)  (0.5, 4.25)

Step-by-step explanation:

(a) The 2-point form of the equation of a line is a good place to start:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

Filling in the point values, we have ...

  y = (8 -3)/(2 -0)(x -0) +3

  y = 5/2x +3 . . . . . . simplify

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(b) Similarly, filling in the point values, we have ...

  y = (3 -4)/(3 -1)(x -1) +4

  y = -1/2(x -1) +4 . . . . . . simplify

  y = -1/2x +9/2 . . . . . . . eliminate parentheses, collect terms

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(c) The lines have different slopes, so are consistent and independent.

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(d) Substituting for y, we have ...

  5/2x + 3 = -1/2x + 9/2

  5x +6 = -x +9 . . . . . . . . . . . . multiply by 2 to eliminate fractions

  6x = 3 . . . . . . . . . . . . . . . . . . add x-6

  x = 3/6 = 1/2 . . . . . . . . . . . . . divide by the x-coefficient

Using the equation for Sidewalk 2, we can find y:

  y = -1/2(1/2) +9/2

  y = 17/4

The point of intersection is (x, y) = (1/2, 17/4).

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.