Question

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Answer 1

Explanation:

Slope of line passing through
`(x_1,y_1)` and
`(x_2,y_2)` is given by,

m =
`(y_2-y_1)/(x_2-x_1)`

From the graph attached,

Slope of the line passing through (-3, 0) and (0, 5) =
`(5-0)/(-3-0)`

=
`-(5)/(3)`

Line passing through a point (h, k) and slope 'm' will be,

y - h = m(x - k)

Since, line passing through (11, 0) is parallel to the line given in the graph,

Slope of the parallel line will be same as
`-(5)/(3)`

Equation of a line passing through (11, 0) and slope =
`-(5)/(3)`

y - 0 =
`-(5)/(3)(x-11)`

y =
`-(5)/(3)(x-11)`

Now satisfy this equation with the points given in the options,

Option (1)

For (1.67, -15.59),

-15.59 =
`-(5)/(3)(1.67-11)`

-15.59 = -15.55

False.

Therefore, given point doesn't lie on the line.

Option (2)

For (-0.33, -13.59)

-13.59 =
`-(5)/(3)(-0.33-11)`

-13.59 = -18.88

False

Option (3)

For (0.67, -18.59),

-18.59 =
`-(5)/(3)(0.67-11)`

-18.59 = 17.22

False

Option (4)

For (1.67, -15.59)

-15.59 =
`-(5)/(3)(1.67-11)`

-15.59 = -15.55

False.

Therefore, none of the points given in the options are lying on the line.