Length of a Line Segment

The coordinates of the vertices of an isosceles triangle are shown. The $x$-coordinate of one of the vertices is missing. Which expression represents the missing $x$-coordinate?

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Find the distance between the point $\left(1,3\right)$ and the origin.

A variable line in a plane passes through a fixed point and meets the coordinate axes at points $A$ and $B$. Then the locus of the mid-point of $AB$ is

What is the distance of point $\left(5, 12\right)$ from the origin?

If a line has the equation $\left(y+4\right)=m\left(x-7\right)$ and it passes through the point $\left(-5,6\right).$ Then find the slope of this line

Amul conducted a survey he cheek locking of ice cream flowered among vanilla, chocolate, strawberry for $350$ Per so people like all $3$Ice cream flavours, same no of people like, chocolate &strawberry. The people who like vanilla & chocolate is $60$ & People who like strawberry & vanilla is$40 of 90$ people like vanilla flavour. If $60$ people do not like any flavour & people who like only chocolate is equal to who like only strawberry .

What is the no of people who like only chocolate flavour. 

The points $A(2,5),B(4,19),C(14,29),\text{ and }D(12,15)$ forms a

The point $(x,2)$ is at a distance of $8$ units from the line $9x+12y+15=0,$What is the value of $x$?

The three vertices of a parallelogram taken in order are $(-1,1),(3,1)$ and $(2,2)$ respectively. Find the coordinates of the fourth vertex.

If the middle points of the sides of a triangle are $(1,1),(2,-3)$ and $(3,4)$, find the centroid of the triangle.

The three vertices $A,B,C$ of a parallelogram $ABCD$ are $(–2,–1),(3,0),(1,–2)$ respectively, find the co-ordinates of vertex $D$.

What is the radius of a circle, if the centre of the circle is at $(2, –3)$ and the point $(–1, –4)$ lies on the circle.

The distance of the point $(12,-9)$ from the origin is-

If the midpoints of the sides of a triangle are $(2,1), (-1,-3),$ and $(4,5),$ then find the coordinates of its vertices.

Let $\alpha , \beta , \gamma , \delta \in Z$ and let $A\left(\alpha , \beta \right), B\left(1, 0\right), C\left(\gamma , \delta \right)$ and $D\left(1, 2\right)$ be the vertices of a parallelogram $ABCD$. If $AB=\sqrt{10}$ and the points $A$ and $C$ lie on the line $3y=2x+1$, then $2\left(\alpha +\beta +\gamma +\delta \right)$ is equal to

Cotyledons are also called-

If the coordinates of the vertices of the triangle $ABC$ be $\left(-1,\mathrm{ }6\right),\mathrm{ }\left(-3,\mathrm{ }-9\right)$ and $\left(5,\mathrm{ }–8\right)$ respectively, then the equation of the median through $C$ is

Vertices of a quadrilateral $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ are $\mathrm{A}\mathrm{ }\left(1,\mathrm{ }2\right),\mathrm{ }\mathrm{B}\mathrm{ }\left(4,\mathrm{ }6\right),\mathrm{ }\mathrm{C}\mathrm{ }\left(8,\mathrm{ }9\right)$ and $\mathrm{D}\mathrm{ }\left(5,\mathrm{ }5\right)$ . Then quadrilateral $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ is

If mid point of $\left(1, a\right)$ and $\left(a+b, 2\right)$ is $\left(-1,\mathrm{ }-1\right)$ then value of $a^2+b^2$ is

The coordinates of midpoints of the sides of a triangle $\mathrm{A}\mathrm{B}\mathrm{C}$ are $\mathrm{D}\left(2,\mathrm{ }1\right),\mathrm{ }\mathrm{E}\left(5,\mathrm{ }3\right),\mathrm{ }\mathrm{F}\left(3,\mathrm{ }7\right)$ . Then sum of lengths of sides of the triangle is