Show that the points (4,3), (6,4), (5,6) and (3,5) are the vertices of a square.
Answers
<div class="shy right"></div>
</div>
<style>
body {
background:#FFFF00
}
.face {
height: 600px;
width: 350px;
position: relative;
margin: auto;
}
.face:before {
content:'';
background:black;
height:122px;
width:95px;
position:absolute;
z-index:6;
left:210px;
top:29px;
border-radius:100% 190% 100% 0%;
transform: rotate(-20deg);
}
.face:after {
content:'';
width:230px;
height:180px;
background:black;
content:'';
transform: rotate(-8deg);
position:absolute;
border-radius:100% 160% 100% 0%;
left:70px;
bottom:-14px;
top:10px;
z-index:5;
}
.forhead, .forhead:after {
content: '';
width: 220px;
height: 181px;
background: #fbc6a3;
content: '';
transform: rotate(-3deg);
position: absolute;
border-radius: 60% 120% 50% 0%;
left: 67px;
bottom: -14px;
top: 21px;
z-index: 6;
}
.forhead:after {
width: 160px;
height: 150px;
border-radius: 150% 174% 159% 100%;
transform: rotate(-20deg);
top: 13px;
left: 59px;
border-top: 15px solid #fbc6a3;
}
.forhead:before{
background:#fbc6a3;
width:60px;
height:10px;
content:'';
position:absolute;
z-index:7;
left:105px;
top:9px;
transform: rotate(13deg);
border-radius:100%
}
.ear {
width:60px;
height:50px;
background:#fbc6a3;
z-index:7;
position:absolute;
border-radius:300% 190% 200% 100%;
transform: rotate(-20deg);
top:110px;
left:285px
}
.cheeks {
background: #fbc6a3;
width: 280px;
height: 100px;
border-radius: 50px 0px 50px 40px;
transform: rotate(-3deg);
position: relative;
content: 'a';
top: 108px;
left:10px
}
.cheeks:after {
width: 297px;
height: 100px;
background: #fbc6a3;
content: '';
transform: rotate(-3deg);
position: absolute;
border-radius: 100% 100% 100% 100%;
left: 1px;
bottom: -14px;
}
.eye {
width:40px;
height:40px;
position:relative;
background:black;
border-radius:100%;
animation: close-eye 4s none .2s infinite;
}
.eye:after {
content:'';
position:absolute;
background:white;
width:15px;
height:15px;
border-radius:100%;
left:17px;
top:12px;
}
.eye:before {
content:'';
position:absolute;
width:70px;
height:60px;
border-radius:100%;
border-top:2px solid black;
left:-20px;
margin-top:-20px;
}
.eye.left,.eye.right {
position:absolute;
top:80px;
left:100px;
z-index:10;
}
.eye.right {
left:190px;
top:90px;
}
.eyebrow {
animation: eyebroani 2s linear .2s infinite;
}
.eyebrow,.eyebrow:after {
position:absolute;
width:20px;
height:60px;
background:black;
z-index:8;
border-radius:15px;
transform: rotate(40deg);
top:10px;
left:90px;
}
.eyebrow:after {
content:'';
transform: rotate(-100deg);
left:19px;
margin-top:-23px;
top:auto;
}
.eyebrow.right {
left:180px;
top:8px;
transform: rotate(50deg);
}
.mouth {
position:absolute;
width:40px;
height:40px;
background:#76322f;
border-radius:100%;
top:180px;
left:50px;
z-index:8;
}
.shy {
position:absolute;
width:0px;
height:0px;
border-radius:100%;
opacity:0;
box-shadow: 0px 0px 40px 20px red;
z-index:8;
left:35px;
top:160px;
animation: shy 10s linear .2s infinite;
}
.shy.right {
left:170px;
top:180px;
}
@keyframes eyebroani {
0% {margin-top:auto}
10% {margin-top:-10px}
20% {margin-top:auto}
30% {margin-top:-10px}
40% {margin-top:auto}
100% {margin-top:auto}
}
@keyframes shy {
0% {opacity:0}
10% {opacity:0.2}
90% {opacity:0.2}
100% {opacity:0}
}
@keyframes close-eye {
0% {
height: 40px;
margin-top: auto;
overflow: auto;
}
5% {
height: 2px;
margin-top: 20px;
overflow: hidden;
}
5.1% {
height: 40px;
margin-top:0;
Answer:
Step-by-step explanation:
The length of all sides are same and the length of both the diagonals are same, therefore the given figure is a square.
The vertices of polygon are A(4,3) , B(6,4) , C(5,6) and D(3,5).
The distance formula is
d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}
AB=\sqrt{(4-6)^2+(3-4)^2}=\sqrt{5}
BC=\sqrt{(6-5)^2+(4-6)^2}=\sqrt{5}
CD=\sqrt{(5-3)^2+(6-5)^2}=\sqrt{5}
AD=\sqrt{(4-3)^2+(3-5)^2}=\sqrt{5}
The length of all sides are same.
The length of diagonals are
The length of diagonals are
AC=\sqrt{(4-5)^2+(3-6)^2}=\sqrt{10}
BD=\sqrt{(6-3)^2+(4-5)^2}=\sqrt{10}
The length of both the diagonals are same.
Since the length of all sides are same and the length of both the diagonals are same, therefore the given figure is a square.