1.

If the distance between the points (-2, -5) and (-6, y) is 5 units, find the value of y.

Answer» Distance between the points (-2, -5) and (-6, y)
`" "=sqrt((-6 +2)^(2)+(y+5)^(2))=sqrt(16+y^(2)+10y + 25)`
`" "=sqrt(y^(2)+10y+41) `
Given that,
` " "sqrt(y^(2)+10y+41)=5rArr" "y^(2)+10y+41=25`
` rArr" "y ^(2)+10y+ 16=0 rArr" "y^(2)+ 2y+8y+16=0`
`rArr" "y(y+2)+8(y+2)=0rArr" "(y+2)(y+8)=0`
`rArr" "y+2=0 or y+8=0`
`" "y=-2 or y=-8`


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