Point (-13 , -4) must lie on the line whose endpoints are (-3 , 2) and (2 , 5)
Step-by-step explanation:
To solve the problem:
- Find the slope of the line from its endpoints
- Then find which point will give the same slope with each end point of the line
The formula of the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where
[tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points on the line
∵ The endpoints of the line are (-3 , 2) and (2 , 5)
∴ [tex]x_{1}[/tex] = -3 and [tex]x_{2}[/tex] = 2
∴ [tex]y_{1}[/tex] = 2 and [tex]y_{2}[/tex] = 5
∵ [tex]m=\frac{5-2}{2--3}[/tex]
∴ [tex]m=\frac{3}{5}[/tex]
Let us find the slope of each point in the answer with the endpoint
of the line to find which point will give the same slope
→ Point (10 , 6)
∵ [tex]x_{1}[/tex] = -3 and [tex]x_{2}[/tex] = 10
∵ [tex]y_{1}[/tex] = 2 and [tex]y_{2}[/tex] = 6
∴ [tex]m=\frac{6-2}{10--3}[/tex]
∴ [tex]m=\frac{4}{13}[/tex]
∵ The slope ≠ [tex]\frac{3}{5}[/tex]
∴ Point (10 , 6) does not lie on the line
→ Point (9 , 7)
∵ [tex]x_{1}[/tex] = -3 and [tex]x_{2}[/tex] = 9
∵ [tex]y_{1}[/tex] = 2 and [tex]y_{2}[/tex] = 7
∴ [tex]m=\frac{7-2}{9--3}[/tex]
∴ [tex]m=\frac{5}{12}[/tex]
∵ The slope ≠ [tex]\frac{3}{5}[/tex]
∴ Point (9 , 7) does not lie on the line
→ Point (5 , 10)
∵ [tex]x_{1}[/tex] = -3 and [tex]x_{2}[/tex] = 5
∵ [tex]y_{1}[/tex] = 2 and [tex]y_{2}[/tex] = 10
∴ [tex]m=\frac{10-2}{5--3}[/tex]
∴ [tex]m=\frac{8}{8}=1[/tex]
∵ The slope ≠ [tex]\frac{3}{5}[/tex]
∴ Point (5 , 10) does not lie on the line
→ Point (-13 , -4)
∵ [tex]x_{1}[/tex] = -3 and [tex]x_{2}[/tex] = -13
∵ [tex]y_{1}[/tex] = 2 and [tex]y_{2}[/tex] = -4
∴ [tex]m=\frac{-4-2}{-13--3}[/tex]
∴ [tex]m=\frac{-6}{-10}[/tex]
∴ [tex]m=\frac{3}{5}[/tex]
Let us check it with the other end (2 , 5)
∵ [tex]x_{1}[/tex] = 2 and [tex]x_{2}[/tex] = -13
∵ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = -4
∴ [tex]m=\frac{-4-5}{-13-2}[/tex]
∴ [tex]m=\frac{-9}{-15}[/tex]
∴ [tex]m=\frac{3}{5}[/tex]
∵ The slopes are equal [tex]\frac{3}{5}[/tex]
∴ Point (-13 , -4) lies on the line
Point (-13 , -4) must lie on the line whose endpoints are (-3 , 2) and (2 , 5)
Learn more:
You can learn more about the linear equation in brainly.com/question/4152194
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