Find the ratio in which the line segment joining the points P(6, 4) and Q(1, -7) is divided by the X-axis.
Answers
Answer:
We have been given the coordinates of the two points. Let these points be A and B
A (6, 4)
B (1, −7)
Let the point lying on the x axis where the axis intersects with the line be (x, y). but as this point lies on the x – axis, its y coordinate will be 0. Let this point be X
X (x, 0)
Let the ratio in which the line gets divided by the axis be k:1
Applying the sectional formula:
If the points A and B have coordinates (x1,y1)" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">(x1,y1)(x1,y1) and (x2,y2)" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">(x2,y2)(x2,y2) respectively. C (x, y) the point dividing this line in the ratio m:n, then according to the sectional formula:
C(x,y)=(mx2+nx1m+n, my2+ny1m+n)" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">C(x,y)=(mx2+nx1m+n, my2+ny1m+n)C(x,y)=(mx2+nx1m+n, my2+ny1m+n)
Here,
x1=6x2=1" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">x1=6x2=1x1=6x2=1
y1=4y1=−7" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">y1=4y1=−7y1=4y1=−7
x=xy=0" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">x=xy=0x=xy=0
m=kn=1" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">m=kn=1
Step-by-step explanation:
I hope it's help you I