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On a number line, the directed line segment from Q to S has endpoints Q at a -8 and S at 12 Point R partitions the direct line segment from Q to S in a 4:1 ratio Which expression correctly uses the formula (m/m+n)(x2 - x1) + x1 to find the location of point R?

Respuesta :

MrRoyal

Answer:

[tex]R =\frac{4}{4+1}(12 +8) -8[/tex]

Step-by-step explanation:

Given

[tex]QS = (-8,12)[/tex]

[tex]Ratio = 4 : 1[/tex]

Required

Determine the expression that correctly uses [tex]\frac{m}{m+n}(x_2 - x_1) + x_1[/tex]

In [tex]QS = (-8,12)[/tex]

[tex](x_1,x_2) = (-8,12)[/tex]

and

[tex]m:n = 4:1[/tex]

Substitute these values in:

[tex]\frac{m}{m+n}(x_2 - x_1) + x_1[/tex]

[tex]R =\frac{4}{4+1}(12 - (-8)) + (-8)[/tex]

The expression becomes:

[tex]R =\frac{4}{4+1}(12 +8) -8[/tex]

Solving further:

[tex]R = \frac{4}{5}(20)-8[/tex]

[tex]R = \frac{4*20}{5}-8[/tex]

[tex]R = \frac{80}{5}-8[/tex]

[tex]R = 16 - 8[/tex]

[tex]R = 8[/tex]

Hence, R is at 8 on the number line

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